Is there a verb that means to inject with poison?
Those are two separate things. The verb form of poison encompasses the latter. From Merriam-Webster:
1 a : to injure or kill with poison; b : to treat, taint, or impregnate with or as if with poison
Curiously, M-W defines envenom as:
1 : to make poisonous
The freedictionary.com defines envenom as:
- to fill or impregnate with venom; make poisonous
Envenomate
(of a snake, spider, insect, etc.) poison by biting or stinging.
‘these observations suggest that the spiders envenomate their prey’
(Oxford Living Dictionaries)