Für den Sommer hat mich ein Professor als Praktikant ___.
Which verbs work here?
"A" and "c" are the same, "c" being a shorthand of "a".
"D" does not apply, because he is not just letting you do something, but accepting you. "B" also does not apply since he is not just accepting you being there, but has taken you on as an employee in a work relationship.
Angenommen means he has taken you into his "home", "workplace" as an associate, or intern. Aka, you are now part of his family. However with families you'd say aufgenommen.
He offered you a job. You applied. He accepted your offer (to go on and work for him).
In German for accepting an offer you'd say. Ich nehme Ihr Angebot an. aka. Angebot angenommen.
Eingestellt would work too but has a different connotation. If you want to say you waited half an eternity and he finally accepted, angenommen would be better, I think. If you just want to be matter of fact about it or talk about somebody else in the third person you can say "He has me as Praktikant eingestellt."
PS: In my opinion German is more clear on what to use when vs. English where you can often have multiple verbs for the same purpose.