Matt - Hopefully this isn't new construction and it was not something you specifically paid for. If it WAS, contact them first and foremost and have the work redone.
Coaxial cable to RCA is the minimum proper way to wire for a sub. It is the industry standard.
Now, knowing that you may not be able to do this, you go on out and pick up some solder type RCA connectors and warm up your soldering gun.... or go buy one.
It should work, but some noise may be introduced on the line - especially over a longer run. Speaker wire is typically not a shielded cable, so you may have some noise. But, if the line is far enough from power cables and it is not that long of a run, then you may have no issues at all.
Using the cable is NOT the issue, the quality of the sound you actually get may be, but we won't know until you have it 100% hooked up... then let us know.