Can a retainer fix shifted teeth?

Retainer: To retain, is to keep in place. A retainer is fabricated to keep orthodontically aligned teeth from relapsing. If the teeth shifted ever so slightly due to a day or two of non-compliance, then yes, it can move the teeth back. If you are asking about an active appliance moving teeth orthodontically, then yes, an appliance can be fabricated to do just that. But a retainer cannot undo major relapse.

Generally Not: A "retainer" is designed to hold your teeth in their current position, so that they don't move in the future. This is especially helpful for people who have had their teeth straightened, as those teeth tend to drift back to their original positions over time. However, some special retainers can produce very small movements in teeth which are slightly misaligned. Your dentist can advise you best.

Magnitude: Depends on the magnitude of the relapse. A very small amount, yes. Anything more will require braces or aligners or active removeable appliances to re-align followed by an intensive retention program. Please see a specialist Orthodontist for evaluation.