Rinse steaks and pat dry. In a 1-gallon heavy plastic food bag, combine steaks, orange juice, soy sauce, garlic, pepper, oregano, and cumin. Seal bag, set in a bowl, and chill at least 4 hours or up to 1 day; turn occasionally.
Weave 2 long metal skewers (18 to 24 in.) parallel through center of each steak. Lay steaks on a barbecue grill over a solid bed of hot coals or high heat on a gas grill (you can hold your hand at grill level only 2 to 3 seconds). Close lid on gas grill. Cook, turning once, until done to your liking, 6 to 8 minutes for medium-rare (cut to test).
Transfer steak to a platter, remove skewers, and cut meat into portions. Add salt and pepper to taste.