I suppose you ask for a step response, don´t you ?
In this case, a practical value is T(response)≈(6...7)R*C.
(In theory, the output reaches the input at infinity).
7*RC is setting time to 0.1% residual error for a first order low pass. Can be a meaningful parameter, but I never found it designated "response time". Unfortunately, wpchan05 didn't manage to specify the requested parameter exactly. I don't see other candidates than tr(10%,90%), which is 2.2*RC, as said, or possibly group delay, which is 1.0*RC for f << fg.