Hello SophieEnglish,
The answer is yes, you can do this with a variety of tissue grafting techniques. One is with fat and the other is with fascia from behind your ear. The first attempt can be made with injecting fat, concervatively, and you may find you like that just fine. The other technique is an open trans-blepharoplasty incision approach. You can place either fat or fascia. I find fascia works a little better.
Now let me say a few things. It's safe but this procedure takes special technical experience and training. Go to an oculoplastic or facial plastic surgeon. Also, be aware that even in the best hands the two sides can be a little uneven and may need minor revisions. The primary reason for this unevenness is not from the surgeon but the grafted fascia. It doesn't have it's own blood supply for about 5 days. During that time it can atrophy in an asymmetric fashion.
Best of luck
Chase Lay, MD