Yes, the first time this happens is in the classic serial "The Vanished Batman" from 1956. Robin takes over after Batman disappears. Commissioner Gordon makes a change to the Bat-Signal.
Batman: Vol 1 #101
He does so again in "The Blind Batman" from 1961.
Batman: Vol 1 #143
Damian Knight calls Batman by placing his emblem in front of the Batman spotlight in Detective Comics #1003
Detective Comics #1003 - 'Medieval'
Poison Ivy and Bane steal the Bat-signal in Batman and Robin (1997) and she converts it into a 'Robin-Signal' to lure him into her clutches.
There's also an 'R-Signal' seen in the Batman: The Brave and the Bold cartoon episode The Color of Revenge!. Note that this shines over the sky of Bludhaven, not Gotham.
And of course, who could forget the Robin Signal from The Lego Batman Movie?