Translation:I also drink tea.
"Either" indicates that there is a choice available between two things, but that you aren't being specific (or don't care) which one. So, "I drink either" means "I drink both of those two things (but not at the same time)" while "I'll drink either" means "I will drink one of those two things (but I'm not telling you which one to give me)".
The confusion here comes from the negative construction, however. This sentence is "I also drink tea.“ If it were negative, we would use "either" and say "I don't drink tea either." However note that either only works this way in negative sentences (and it still has the other meaning, so if I said "I don't drink either tea", it would mean there were two teas to drink but I don't drink them, and I could even say "I don't drink either tea either" which has both meanings of "either" in it).