Move "R series" to connect from the "bottom" of the inductor (L1, R1, and C1) to ground, then put your oscilloscope across that resistor.
Connect the pulse or square-wave generator from the "top" of the inductor to ground.
Note that the output impedance of the generator will also affect the current in the circuit, but the voltage across "R series" will be an accurate measurement of the actual current in the total circuit, so long as that resistor is much less than the oscilloscope input resistance. Also, the input capacitance of the oscilloscope will have an effect, but only at very high frequencies where its reactance is comparable to that small resistor.