This is a very complicated topic to write about. Can a priest be a socialist? The simplest answer would be "no". But it is important to look a little bit deeper. I know that many people believe that Jesus Christ and the social justice present in the Catholic Church are very close to socialism but there is one very important difference.
First of all socialism doesn't accept free will. Jesus Christ respects and emphasizes free will.
Secondly, in socialism a person depends on the community and all the decisions have to serve it. There is no personal responsibility. The main group decides what is good for a single person.
The Catholic Church doesn't serve the community. It is the community of the Church that serves God. Social justice doesn't take away a single person's responsibility for their own actions (matter of a sin).
So, it is time to ask: could a priest be a socialist? There is only one answer: no. Socialism is against God and all the values offered to us by our creator. Social justice, a very unfortunate English expression (it should be: Catholic teaching about society), is not about disabling the poor or the unfortunate, but about a just approach to social problems.
What is justice? Lustitia est constans et perpetua voluntas ius suum cuique tribuere - Justice is the constant and perpetual wish to render to each one his rights. A priest needs a correct understanding of those rights. A right is not what I want but it is what belongs to me because I am a person. It is very unfortunate that many people, including priests, lost this understanding of justice and they replaced it with a general approach that everybody should have the same and in that way be equal. It is not justice, it is an ideal socialism that sooner or later turns into a dictate.
Jesus Christ wasn't a socialist. He always respected our personal choices and decisions. He always let us carry on all our responsibilities. His love doesn't disable us but makes us more responsible for everything we do.