Is there a way to get out of a online leasing agreement that you don't recall signing for?

You could send them a written demand for them to either provide you with proof that you provided informed consent to enter into a binding agreement or confirm that there is no binding agreement. In order to enforce any agreement against you they should at least need to prove that you provided informed consent to enter into it.

How do you not recall? Was this years ago or something? Are you saying you don't even know the company at all and never even went to the site. Or just that you may have visited it in contemplation of signing up but you believe you never clicked through to the end? Seems it would be very reasonable and easy for them to produce a copy of the signed contract so you can then review it (or better yet have it reviewed by an attorney). Are they suing you? Or just demanding that you take possession of an apartment/be on the hook for all rent until the end of the term?

If you in good faith do not believe that you ever ratified such an agreement, you have the right to demand proof that you in fact did so with a genuine, bona fide signature. If the property cannot produce such proof, you are not legally bound; if the property can produce such proof, you would be bound unless/until some signed and written modification could be ratified, thereby revoking the prior agreement. Best wishes in an amicable resolution of this matter.