You're not the only one this happens to, exercise is one of the best natural laxatives.
What I found interesting is that any physical activity can help prevent constipation, because it isn't just the physical rebounding of the gut from running which loosens things up, the colon also gets stimulated so it can both absorb the nutrients you'll need while exercising and expel waste more efficiently. So, any exercise will actually have a laxative effect.
From the Mayo Clinic:
Physical activity increases muscle activity in your intestines. Try to
fit in exercise most days of the week.