Yes, Austin, Texas is larger than Washington, D.C. in population.
Austin has been one of the fastest-growing large U.S. cities for decades, while D.C.'s population is constrained by its fixed 68-square-mile district boundaries. However, the Washington-Arlington-Alexandria metro area (~6.3 million) dwarfs the Austin-Round Rock metro (~2.4 million). So "larger" depends on whether you compare city limits or metropolitan regions.