Yes, regular physical fitness routines will indeed make a difference on bone structure and growth as well as muscle mass giving net result as an increase in shoulder distance. The younger you are as you begin, the greater the effect will be. Specifically, weight training and other anaerobic and high impact routines will have the greatest effect on both bone and muscle growth. This, however, needs to be consistent training over a long period of time in order to realize the effects long-term.
The goal is to naturally increase your growth hormone (GH) levels as osteocytes and osteoblasts are stimulated by GH and by mechanotransduction. Actual bone length may not be effected at all and may have more to do with genetics. See my other answer here (relating to wrist size, but also relevant for other bones and muscles) for a detailed explanation. HINT: Read the section entitled "Detailed Explanation of Bone Growth".
Diet also plays an important role. You need to have enough protein as well as many other nutrients in order to support and maintain the muscles and bones.
Just about any upper body workout involving the shoulders, chest, or upper back overtime will give the impression of a greater shoulder distance and increase bone density and growth overtime. You should, however, not endeavor to make this your main goal. Ideally, overall health and fitness and proportionate body strength should be the main goal to strive for. Besides, as your leg and glut muscles are the largest in your body, they will therefore have the greatest net effect in increasing your GH levels.
Relation between upper body workout and wrist size