Your 7.62x39 rifle doesn't have the long distance capabilities of larger cased cartridges. But you'll do OK if you are in a good area, have patience, and watch your distance carefully.
I've been successful taking elk with my .308 and 30-30 rifles.
Plenty of hunters think elk are armor-plated but they're not at all. It's true that elk do not react to a good chest shot same as smaller animals. My advise is to keep shooting into the chest organs until the animal is down.
Good hunting to you.
Fire up the grill! Deer hunting IS NOT catch and release.