There is nothing in the New Testament that suggests that Jesus was a vegetarian. However, some biblical scholars believe that there is evidence (but not proof) that Jesus belonged to the Jewish Essene sect. They followed religious law, including a strict vegetarian diet, i.e. no meat. It is known that his native tongue was Aramaic, which is probably why people connect him with that particular sect.

The bottom line is that PETA is a domestic terrorist organization, and misleading the public with severely biased and unproven claims is really one of their most common tactics.