Running, and cardio vascular exercises in general, can (and often do, especially for extremely dedicated female runners) have an impact on a woman's period. As long as you are keeping your running to a balanced amount each week, and making sure you are properly refueling and consuming plenty of of calories from all three macro nutrient groups (i.e. a well balanced diet of proteins, fats, and carbs) then your period probably will not be effected. However, many female runners face the loss of their period during intense training periods in which they are running and exercising a lot and not eating enough. Even if they are working with a dietitian or nutritionist who has created a well designed meal plan for them that fuels them for the excessive amount they are running, they can still lose their period. (If you are interested, check out elite runner Tina Muir's website, tinamuir.com. Tina ran competitively for Great Britain, but shared her story with the public on her blog and through social media about how she lived for many years without a period. When it came time for her and her husband to start a family, she put running aside completely and focused on eating enough and getting her period back.)
This all has to do with the fact that a woman's period is not a "necessary" function in order for the body to stay alive. When we fail to feed ourselves enough or put our bodies under too much stress (this might be mental stress due to overwhelming life circumstances of physical stress brought on by over exercising), then they start to turn off the functions that are not vital to staying in live, so that it can focus all the energy it DOES have on keeping up with the systems that ARE critical to life. Essentially, too much running can mean not enough leftover energy to have a period.
Keep in mind going into race day that your period might mean you feel a bit more tired and bloated than usual. You will need to make sure you still eat enough carbs in the days before to fuel your race (which you might find yourself craving extra of anyways! Don't deny those period cravings too much because they are your body telling you what it NEEDS to not just survive, but thrive). The best way to cope with the arrival of your period on race day is to prepare yourself mentally that things might be a little "off" that day - then go out there and race!