Try a Garbage Bag
If you have to wait outside in the rain before the start of a race, a big trash bag with armholes and a neck hole cut out can help you stay dry. You can take it off and throw it to the side once you get moving. You can even train with it as well. SO what if you look like a moving bag of garbage. IF you're not having a good day and someone asks how you're feeling. Tell 'em "I feel like garbage today".
The hardest part of running in the rain is often just getting started. Once you begin running and warm up, you may find that you actually enjoy it! So what if you get wet. Remember when it was 90' and 100% humidity? The rain can feel refreshing.
And don't forget to dry out your shoes
When you get back from a wet run, take off your running shoes and stuff them with crumpled balls of newspaper. This helps the shoes keep their shape, and the paper draws moisture away from the shoes.