The short answer is yes, Jesus did drink wine, and so did his apostles. Jesus even seems to encourage the drinking of wine at the wedding feast in Cana recorded in John 2:1-11. On that occasion he miraculously turned water into wine after those present ran out of it to drink.
There was no law to abolish the drinking of wine; only the Nazarites were commanded to never drink it as he “shall separate himself from wine and strong drink” (Numbers 6:1-4). This is the only group and instance within the Bible that anyone is commanded not to drink wine, however Jesus was a Nazarene (someone from Nazareth), hence not a Nazirite.
Nevertheless, Jesus turning the water into wine at the wedding feast does not prove that he did in fact drink of it, but there is no reason to suspect that he did not. If he would seemingly encourage it that then illustrates that he does not condemn it or think of it as inherently sinful. It would, however, become sinful should it be abused to the extent of drunkenness, at least judging by what Paul writes in Ephesians 5:18: “And do not get drunk with wine, for that is debauchery, but be filled with the Spirit.”
Perhaps the most illustrative of verses that give us a reason to believe that Jesus did drink it is that found in Luke 7:33–44 where he compares himself to John the Baptist in order to answer a charge. He answers: “and you say, ‘Look at him! A glutton and a drunkard, a friend of tax collectors and sinners!’”
Basically, Jesus says that he was being falsely accused of being called a drunkard by his enemies when he actually was not. It would be unlikely the case that his enemies would accuse him of drinking wine if he never did in fact drink it, Jesus also doesn’t claim that he never drank wine.
Another suggestive line of evidence is that of the Jewish holy days, that of the Passover celebration. Such occasions certainly included wine drinking, and the relevant texts even indicate this by repeatedly asserting the term “fruit of the vine.” It is almost certain that Jesus would have drank from the Passover cup (Mark 14:23) where he instituted the Eucharist. So, what would this wine have actually been like?
The wine the Jews would have drunk in those days would be fermented, and not grape juice as some have suggested. Fermented wine would have always been served at weddings, and on other special days and occasions. This would be precisely because 1st century Jewish people had no means of being able to preserve juice. They had no preservatives or other modern processes to keep grape juice from fermenting. So once they harvested the grapes for the year and stored the juice in skins the fermentation process would naturally begin. After a long while of storing the grape juice in containers one would get fermented wine.
This is further suggested in scripture when the apostles are falsely accused of being “drunk on wine” in Acts 2:13-15. Their opponents would not use this as an accusation if they were drinking grape juice. Further, Peter replies that it was too early for them to be drinking so much wine, hence he is saying that they were not drunk. If Jesus ever forbade the drinking of wine then we’d have good reason to believe that his apostles would not drink.
So, in concluding Jesus did drink wine, perhaps at the wedding in Cana and almost certainly at the last supper. Jesus certainly admits to this in Luke 7:33–44 by never denying the charge by saying he drank wine, what he denied was the false accusation of being a drunkard. The wine he and his apostles, as well as other 1st century Jews, would have been fermented, alcoholic.