Can I play soccer a week after injuring my groin?

Depends on injury. Groin injuries can be from many sources, a muscle strain, a tendon tear, an injury inside the actual ball and socket joint of the hip or even a hernia. If you are completely pain free, and are able to perform all ball drills, running and cutting drill and are able to work into 3v3 or 5v5 drills without any pain, then you can play. Make sure you warm up well and get a good sweat going before out.