The 26-year-old midfielder joined the Shrews in the summer but has made just five starts for the club.
Shots boss Dean Holdsworth told the club's official website: "Asa is a player that has been working in a division above us which is good experience for him.
"He is coming to us at the right time. He has a lot of desire to show that his career is going in the right direction.
"He is a good competitor and has a goal or two in him too."
Hall began his career at Birmingham before moving on to Boston, Luton and Oxford.
- Sports & Recreation
- Employment & Career
- Dean Holdsworth