This isn't possible in the sense of being able to directly share AA dimensions to Target through a server-side integration. It depends a bit on the use case but one option would be to share AA dimensions to Target client-side through page parameters
i.e. if you've mapped dataLayer.something to eVar53 as part of your AA implementation then you could very easily map dataLayer.something to a page parameter that is sent to Target. At that point you could then use profile scripts on that ingested data