The short answer is Yes, but not before Christ returns. It is dogma that Jesus Christ did not give His Church the authority, nor the ability to ordain women as priests. So a woman cannot be a validly-ordained priest. A Bishop is a kind of priest, so women cannot be priests. And a Pope is a kind of Bishop and a kind of priest, so women cannot be Pope. Any woman claiming to be a Pope is an antipope, by definition.
However, the question of women deacons is open. The Magisterium has never defined that women cannot be ordained as deacons. Historically, there were women deacons (deaconesses), but they were not ordained. They did not receive the Sacrament of Holy Orders. The historical case, though, does not settle the question. The Church may still have the authority to ordain women as deacons. The fact that She has never done so before does not exclude the possibility. The Church is on a journey toward Heaven and toward the Return of Christ, and things happen on a journey. Things change. There is no rule given to the Church by Christ saying never change. In fact, Jesus himself said the opposite:
[John]
{16:12} I still have many things to say to you, but you are not able to bear them now.
{16:13} But when the Spirit of truth has arrived, he will teach the whole truth to you. For he will not be speaking from himself. Instead, whatever he will hear, he will speak. And he will announce to you the things that are to come.
{16:14} He shall glorify me. For he will receive from what is mine, and he will announce it to you.
{16:15} All things whatsoever that the Father has are mine. For this reason, I said that he will receive from what is mine and that he will announce it to you.
My opinion is that the Church does possess the authority and ability to ordain women as deacons. But we shall see what the Magisterium decides. If the Magisterium decides that women can be ordained as deacons, expect to see many conservative Catholics depart from the Church, again accusing the Roman Pontiff of heresy.
After Christ Returns
It is possible, theologically, for the one holy Catholic and Apostolic Church to have validly-ordained women priests after Christ returns. The teaching is not that women cannot be ordained, but that Christ did not give His Church that authority. So when He returns, he may give the Church that authority.
And based on Sacred Scripture, I believe that He will do so.
[Revelation 20]
{20:1} And I saw an Angel, descending from heaven, holding in his hand the key of the abyss and a great chain.
{20:2} And he apprehended the dragon, the ancient serpent, who is the devil and Satan, and he bound him for a thousand years.
{20:3} And he cast him into the abyss, and he closed and sealed it, so that he would no longer seduce the nations, until the thousand years are completed. And after these things, he must be released for a brief time.
{20:4} And I saw thrones. And they sat upon them. And judgment was given to them. And the souls of those beheaded because of the testimony of Jesus and because of the Word of God, and who did not adore the beast, nor his image, nor accept his character on their foreheads or on their hands: they lived and they reigned with Christ for a thousand years.
{20:5} The rest of the dead did not live, until the thousand years are completed. This is the First Resurrection.
{20:6} Blessed and holy is he who takes part in the First Resurrection. Over these the second death has no power. But they shall be priests of God and of Christ, and they shall reign with him for a thousand years.
We are not now in the time when Satan is bound for a thousand years. That is obvious from all the sin and harm in the world, and all the sin among members of the Church. Satan is active in the world today. So that time when Satan will be bound is in the future. It is the long time of peace and holiness that occurs after the tribulation is completed. (Jesus does not reign on earth during that time, so this is not an example of the heresy of millenarianism).
The souls of those who were martyred during the Antichrist’s reign are resurrected (along with all past martyrs and Saints). This is the First Resurrection. The general Resurrection is a later event. These martyrs did not accept the mark of the beast (the Antichrist), so this time of peace and holiness begins after the fall of the Antichrist.
Those who receive the First Resurrection include women, for the Church has many women Saints and martyrs. But Sacred Scripture tells us that “they shall be priests of God and of Christ, and they shall reign with him for a thousand years.” So the men and women of the First Resurrection are ordained as priests. This text from Revelation tells us that the Church will have ordained women priests during the time period after the second part of the tribulation. However, these men and women of the First Resurrection have the Beatific Vision of God. They are sinless and holy. They have all the gifts given to those of the Resurrection. Ordinary women are not given the priesthood, as far as we can tell from this passage, even in that future time.
Ronald L. Conte Jr.
the reproach of Christ 
Mes chers amis,
Envers et contre tout, restons fidèles à l’Eglise de toujours, soyons vraiment traditionalistes, convertissons-nous à chaque instant, restons unis et prions le plus souvent possible le Saint Rosaire, ou, au moins le chapelet. Ayons aussi une vie intérieure intense,quitte à en accepter certains dégâts collatéraux et vivons les uns pour les autres… Un pauvre pécheur.
I can’t see how the ordination of women to the diaconate would be permissible if after over 2000 years no women has ever been ordained. Its been the constant teaching of the Church that men only can be ordained. I have never read anything to the contrary, although its not defined as infallible, but I would say non-infallible. Canon 1024 says only men can be ordained. Ludwig Otts book on Dogma specifies only men can be ordained. In the Catechism below they are talking about sacred ordination in general meaning all 3 degrees of the Sacrament. The 3 ordinations form but one Sacrament.
CCC:
VI. WHO CAN RECEIVE THIS SACRAMENT?
1577 “Only a baptized man (vir) validly receives sacred ordination.”66 The Lord Jesus chose men (viri) to form the college of the twelve apostles, and the apostles did the same when they chose collaborators to succeed them in their ministry.67 The college of bishops, with whom the priests are united in the priesthood, makes the college of the twelve an ever-present and ever-active reality until Christ’s return. The Church recognizes herself to be bound by this choice made by the Lord himself. For this reason the ordination of women is not possible.
The Magisterium infallibly teaches, in Ordinatio Sacerdotalis, that the meaning of the teaching in Tradition and Scripture is that priestly ordination is reserved to men. So you cannot say that “Its been the constant teaching of the Church that men only can be ordained.” The Magisterium has issued a decision on the correct interpretation of Tradition, and it excludes women from priestly ordination. The absence of a decision on whether women can be deacons is not definitive or exclusive. It remains an open question.
On the point about 2000 years, it was probably prior to 2000 BC that Abraham established his covenant with God, which led to the establishment of the Old Testament laws. Yet Christ dispensed the OT disciplines (not the teachings) when He arrived. So changes can occur after a long time.
Also, Canon Law is the current discipline, not a definitive teaching. There is not even a non-infallible magisterial teaching that says women can never be ordained as deacons because….[whatever the reason might be]. They cannot currently be ordained because question is open. But no teaching at any level of the Magisterium settles the question.