The reception must be done by a priest. I checked the RCIA texts, and there’s no provision made for a deacon to do this.
Having said that, I think there might be a possibility for the bishop to dispense from the rubrics to allow this to happen in very unusual circumstances, such as mission territory or other extreme situations. Even if possible, it would require a dispensation from the bishop. I say “dispensation” because the bishop cannot simply delegate that function to a deacon.
The RCIA norms (paragraph 481) reminds us that it is reserved to the bishop himself to receive already-baptized, but that he can delegate this to a priest. It specifically says priest, not priest or deacon.
We all know that deacons can baptize. There’s a principle in law that says that whoever can do “the greater” can also do “the lesser” or to put that another way, whoever can do “the whole” can do “any part of the whole.” So, for example, if a visiting priest has been delegated by the pastor to perform a baptism, he does not need the specific permission to do the anointing with Chrism which is a part of the baptism rite. He can do the whole, so he can do all the parts.
As far as the theology is concerned, I think it’s possible for a deacon to receive converts into the Church, based on the fact that it’s possible for him to baptize adults. He can do the greater, therefore he can do the lesser.
When it comes to receiving previously baptized adults, it comes down to the simple fact that there’s no provision in canon law, nor in the RCIA statutes for this to actually happen. Just because it’s possible, that doesn’t make it licit.
Again, I think that the bishop can grant a dispensation to allow this to happen, but it would have to be very unusual circumstances.
That’s a long way of saying that it’s possible, but not very likely.