Yes, Jesus did drink alcohol by his own admission.
In Luke we read a quote from Jesus himself that says:
Luke 7:33-34 “For John the Baptist came neither eating bread nor drinking wine, and you say, ‘He has a demon.’ The Son of Man came eating and drinking, and you say, ‘Here is a glutton and a drunkard, a friend of tax collectors and sinners.’”
This is obviously NOT a reference to unfermented grape juice, based on the choice word “drunkard”.
It is important to note that this verse does not say that Jesus was a drunkard, but rather that his mockers (Pharisees) called him a drunkard. One only needs to watch a minute of a contemporary political debate to understand how such forms of mud-slinging turns innocent facts into juicy, exaggerated lies. However it is clear that Jesus made a straight-forward admission to drinking wine while arguing against the Pharisees who were trying to expose fault in Him. It is apparent that His drinking of wine was not something that we was ashamed of (Jesus did not sin), nor something that he would not openly admit to His accusers.