What is Waveform of current in rl series AC circuit when operated for first time i.e. from time t =0?
Asssuming your circuit to be



And simulating it, we got



This is the voltage over the resistor, but the waveform is right also for the current.

There's a transient which fades off and soon the current is the same which can be calculated using the voltage, frequency and impedances.

If you need a general formula of the current, you can derive it most easily using the Laplace transform. It's the sum of exponentially dying DC current and the continuous sinusoidal current. The time constant of the death is L/R.

The case is a common example in elementary level textbooks that teach how to apply Laplace transforms to transients in electric circuits.