Submit a sample of your popcorn ceiling to an asbestos testing facility. You are more likely to have asbestos in your ceiling if your ceiling was installed before 1979. If you do have asbestos, you need to consult a licensed asbestos specialist for advice.
Scrape off the part of the ceiling surrounding the crack to widen it so the space around the crack extends about 3 inches on all sides of the crack. Use a stiff putty knife until you reach the paper surface of the ceiling's drywall.
Spread paintable caulk with a putty knife over the enlarged crack to fill it.
Apply latex primer to the problem area with a paintbrush once the caulk is dry.
Spray popcorn texture over the fixed area. You can buy popcorn texture spray in aerosol form at home improvement stores.