No, they were not.
Many think they were because of this Scripture reference:
“And all those who had believed were together and had all things in common; and they began selling their property and possessions and were sharing them with all, as anyone might have need.” Acts 2: 44-45
The reason early Christians sold everything they had was because they took Jesus’s warning seriously.
“But when you see Jerusalem surrounded by armies, then recognize that her desolation is near. Then those who are in Judea must flee to the mountains, and those who are in the midst of the city must leave, and those who are in the country must not enter the city.” Luke 21: 20,21
Therefore, soon after Pentecost, Christians started getting rid of everything they owned in Judah or Judea with an eye towards leaving the area before the day of retribution caught up with them. Read Where is Satan Now? for the sequence of events.
Furthermore, sharing with others less fortunate has always been a Christian mandate, not a communist one.
On the other hand, the whole idea of communism is to steal from regular folks in order to enrich the leaders of the movement, while the centrality of its tenets is the hatred of Christianity.
Communism was created by Jews who hated Christians, and that’s why the first move of any communist regime is to try to stifle Christianity.
The Jewish Marxist Bolsheviks, who took over the Russian government in the 1910s, killed 66 million Christians, including 200,000 members of the Christian clergy, and destroyed 40,000 churches. And Islam is the problem? See The Truth about the Conflict with Russia.
So, nope. Early Christians were not communists. God forbid.