4 of the 5 go-kart venues Go Karting USA tracks in Oregon host birthday parties, based on what each venue publishes and what visitors describe. Most of them cluster around Portland.
Party bookings work differently from walk-in racing: expect a reserved room or area, a set number of races per guest, and a deposit. Weekend afternoon slots go first, so start calling two to three weeks out — and confirm the height rule for the youngest guests before invitations go out, since it varies venue to venue.
Pat's Acres Racing Complex, K1 Speed Bend, Sykart Indoor Racing and 1 more — all listed below with ratings and locations.
Portland (2).
Two to three weeks for a weekend slot, more around school holidays. Party rooms and group race slots are reservation-based at essentially every venue, and afternoon weekend times fill first.
Go Karting USA lists 5 operating tracks in Oregon — see the full Oregon guide for all of them, not only birthday parties venues.