No, he wasn’t.
That is to say, there is not a shred of evidence to make us think that he ever was—and quite a lot of evidence to the contrary. For some reason, though, many pro-vegetarian websites claim him as one of theirs.
In his youth, Darwin bagged pheasants and partridges by the score. At university, he was a member of a social dining club called The Gluttons, who specialised in eating strange meals. He became very sick after one infamous Gluttons dinner of brown (tawny) owl. During the Beagle voyage, Darwin also ate, amongst other creatures, Galápagos tortoise, puma, and rhea. Furthermore, his wife’s Recipes book (Amazon uk | .com) also contains numerous meat dishes.
But the real clincher is to be found in the Sir Francis Darwin’s reminiscences about his father:
Latterly he gave up late dinner, and had a simple tea at half-past seven (while we had dinner), with an egg or a small piece of meat.
So, Darwin certainly wasn’t a vegetarian in his latter days.