While there are insoles and inserts you can match with your running shoes; the ideal option is to get a pair of running shoes that fit your needs and supports your arches without any additional accessories.
If you need further support, there are also running shoes with arch support on our list that are compatible with extra insoles--but keep in mind that this may add additional weight to your shoe, which may drag you down--especially if you like to run long distances.
Bear in mind that people with high arches are prone to developing plantar fasciitis so it's smart to consider plantar fasciitis inserts in advance.