Per a note at Wikipedia talk: Bots on enwiki, there's currently no way of allowing a BotPassword or OAuth authenticated user to merge histories. Seems like it'd be a good thing to add in general, along with the other administrative grants. It doesn't look like the mechanism for doing this is too complicated - I could easily be wrong, but seems to me it's just a change to DefaultSettings.php - but then it does need to be internationalised, which will be the holdup for it.

I'll happily put together the change to add the grant itself, though.