Yes, you can! No smoker, no problem.  You will need a smoker box (affiliate link) filled with wood chips to grill your burgers with a similar smoky flavor. Place it in the center of the grill and place your burgers around it to infuse the most flavor. Check out this article on how to use a smoker box. When using a smoker box, you won't be using pellets, you'll be using wood chips so be sure to keep that in mind when buying your supplies.