In short, no.
Running and other outdoor activities can be beneficial to your physical and mental health, and boost your immune system. The exposure time is too short (less than 5 minutes) assuming you keep moving and the great outdoors provides ample ventilation. You can still practice social distancing during outdoor activities.
Of course, you should always follow guidelines in your city/state when determining whether you should wear a mask outside. In our state of Illinois, you can find out about the recent state wide mandate here: https://www.illinoispolicy.org/what-illinoisans-need-to-know-about-the-may-1-mask-mandate/
https://www.cbsnews.com/news/running-coronavirus-pandemic-social-distancing/