How can I calculate time constant and charge time of RRC circuit?
There are two time constants here.  One is when the input is driven and the other when it is open.

Probably the input is driven high, then left to float low.  When the input is driven, you assume it has 0 impedance to ground.  Note that this impedance is parallel to R1.  What is R1//0?  When the input is open-circuit, then it has infinite impdance to ground.  The effective resistance seen at the top of C1 to ground should be obvious in that case.