No, you can't use a present perfect here. Of the four options, 'joined' (past simple) is the only possible answer.
The speaker is using a time phrase beginning with 'since xx' to specify WHEN he or she first met Dr Jackson. The reply could be "since 2008" or "since last March" or "since we were children". These are all specific points in time. The past simple tells us when something happened; the present perfect does not. This is why A is wrong.