Depends on what kind of polishing you have in mind. You could put a LOT of elbow grease in it and do it by hand, or you could buy yourself a cheap rock tumbler.
....Either that or just smear it with Butter-Flavored Crisco!
You can polish it. But why? It is not precious, really pretty common. You could probably find a similar stone in a $1 package of polished stones at more Dollar Tree stores.
I know it's not valuable, but it is a nice crimson red. I've seen pictures of polished jasper online and they look really neat. It's nice unpolished as well. But yeah if it's too much trouble than I won't. I wouldn't buy a tumbler for the one and O KY rock I'm ever going to polish.