Manchester United trainee Rothwell, 21, has penned a two-year deal.
The attacking midfielder made seven appearances in all competitions during a loan spell with Barnsley last season.
Maguire, 27, has signed a one-year deal after playing 25 games last season during a loan spell and subsequent short-term move from Rotherham.
Find all the latest football transfers on our dedicated page.
Oxford United have signed midfielder Joe Rothwell on a free transfer and agreed a new contract with striker Chris Maguire.