Many states and provinces include stainless steel rebar in their specifications for bridge design & construction.
ASTM A955 is the main Standard for stainless steel rebar in the USA. The fundamental differences are that the profiles and grades (strengths) follow their respective carbon steel standards. ASTM has a corrosion test included. This is manufacturer-specific and not alloy designation specific.
Common US specifications, published by ACI and ASTM, are:
American Concrete Institute: “ACI 318-14 Building Code Requirements for Structural Concrete and Commentary“, ISBN 978-0-87031-930-3 (2014)
AASHTO M 334M/M 334, Standard Specification for Uncoated, corrosion-Resistant, Deformed and Plain Chromium Alloyed, Billet-Steel Bars for Concrete Reinforcement and Dowels