Remember that S-parameters are the ratio of one voltage to another. So, you can obtain the magnitude of S21 very easily (Vout/Vin). You could also get the phase information if you monitor both input and output simultaneously and phase match your inputs (delay compensation).
Getting S11 and S22 are much more difficult, since you don't have a way of separating the forward and backward traveling waves. You might be able to cob something together if you used a directional coupler, then monitored the signals coming off of the transmitted and reflected ports. Phasing would be tricky, but you could get |S11| and |S22| pretty readily that way.
In all cases, you'll need to set up a sinusoidal signal generator to dwell at one freq... take measurements with the o-scope, then shift to a new freq, take o-scope measurements, and repeat until you've swept your entire range of interest.