They certainly do in New Jersey! I have several renters I am working with at present. There is a fee involved so be sure to find out how that works. In New Jersey it is not at all unusual for landlords to require the tenant to pay the fee. Everything in real estate is negotiable, however, so ask your agent to explain thoroughly how it works in Washington.
Bottom line, though, we find the best rentals and the best tenants work with realtors. Busy professionals just do not have the time to do all the legwork themselves and will happily pay a realtor to do it for them.