I'm not sure what you mean by sprocket. If you mean chainring (front gear), then no they are not compatible. You'll most likely need a whole new crankset because many cheaper cranksets have the chainrings riveted to the spider rather than bolted and therefore are permanently attached.
On lower end cranksets the chainrings are riveted or welded on and cannot be replaced without replacing the entire crankset. On better cranksets the chainrings are attached by bolts at standard locations and are individually replacable.
I can't see enough detail from your photo but I'd guess that you have the wrong kind.