Is there a procedure to tighten the skin under the eyes?

tough to make a recommendation without a picture.  If you want to just improve the texture of the skin, you would probably do well with some sort of laser resurfacing.  The type of laser will depend on your skin texture and color.  You might also benefit from some filler.   

Of course you have handicapped us by not providing a photograph so it would be speculative to recommend specific procedures.  Consider reposting with photographs.  Remember as you look for a service, less is often more.

I dont see a photo attached to this question so I will answer generally.  To improve the quality of the eyelid skin and also to tighten the skin I would recommend a laser resurfacing.  The laser I like the best for this area is the fractionated CO2 followed by an erbium laser at the same time.  This gives a tightening and also gets rid of fine lines and brown spots.  Healing is about 1 week.

There are several options to tighten the skin under the eyes.  The best option for you will depend on your particular concerns.  Two common options are surgical interventions and lasers.  See a board certified plastic surgeon in your area to discuss your concerns and explore the option best for you.

There are many options for smoothing and tightening the lower eyelid skin, depending on the nature and degree of the problem. You could benefit from a quality skin care program and peels only or perhaps a little more of an effect could be had from Fraxel laser treatment or a more significant change from CO2 laser resurfacing. It is also possible that a lower eyelid blepharoplasty might give you the best result depending on the amount of skin excess and whether there is a degree of puffiness related to excess fat in the lids. Definitely need to see an experienced Plastic Surgeon to find out your best treatment plan..

There are several procedures available for improving the quality of under eye skin.  You doctor will make a recommendation during you exam.  If you are looking for a conservative approach, consider Retinol based creams which will improve the skin quality around your eyes and stimulate collagen production. Other treatments to consider would be Fractionated laser for fine wrinkles around the eyes, as well as Ultherapy or ThermiSmooth to tighten the skin.  If the area looks hollow,
Restylane injections might be recommended to bring you a much
smother appearance of the under eye area.

Non-surgical options for improving the skin under your eyes include laser resurfacing, TCA peels, and filler (i.e. restylane). Without seeing a photo and examining you in person, it would be difficult to make a specific recommendation to you.