Yes, you can, on most major carriers. Just call the airline's 800 number or check the website for information. A normal gift cert. has a dollar value; the recipient can use it to take that much off whatever fare they wish to purchase.
Since you want this for your parents, I'll also mention that some legacy airlines offer "senior coupons" that can be used on any flight. Those are only useable by persons of a certain age, and the deal is that you pay a set dollar amount and get a certain number of flight coupons that can be used over a certain period of time. You purchase what is essentially a book of them, and each coupon is good for one domestic flight. These are a pretty big investment, but I know seniors who travel often who find that the system is a money-saver for them.
