My entire aloe plant ripped off of the root system. Is there any way I can save it?
It looks like there are still roots on the top portion of the plant. If that's true, you can plant that part. Water sparingly until it makes new roots. Don't worry if it wilts for a little while it reestablishes itself.
It almost looks like the base of the plant may be soft/rotten. If that's the case, cut off the bad parts. If the meristem, the knot at the base of the leaves, is damaged or destroyed it can't/won't re-root. Aloe can't be rooted from leaf cuttings like other succulents.
This document discusses rooting leaf cuttings in succulents.
Note the distinct lack of Aloe information.