Motorists are ignoring no-entry signs to slash travel times by making rat runs across a new bridge that links Rhodes and Wentworth Point in Sydney's west.

Three weeks after it was opened to cyclists, pedestrians and buses, motorists have been spotted illegally crossing the 300-metre Bennelong Bridge to avoid a round trip of about 8 kilometres between the two suburbs.

Local residents have urged Roads and Maritime Services to fast-track the installation of cameras to deter motorists from crossing the $63 million bridge.

Wentworth Point Community Central president Bronwyn Evans said a few cars had already been seen flouting the rules and crossing the bridge to avoid the round trip.