You probably can.
Your orthodontist would first make sure that there are no other issues such as gum or bone loss in the area. If there is, working closely with a periodontist (gum specialist), we can usually close spaces successfully to assure long term health of your teeth and gums.
After space closure, which could be done with braces or Invisalign (depending on your case), I would recommend that you get a permanent retainer placed, which is a small wire glued to the back of your front teeth to prevent them from coming apart again.
Feel free to upload some pictures if you'd like me to take a closer look.
Hope it helps!
Agustin Drubi, DMD