For a specific project, a copy of the prevailing wage rates can be found in Section 00830 of the Project Contract. A copy should always be accessible to the workers on site, to whom the rates apply.
For a copy of the latest prevailing wage rates (not specific to a City project), you can visit this website: http://www.wdol.gov/wdol/scafiles/davisbacon/tx.html. The City of Austin uses Travis County rates.