How to measure capacitor value using an LC circuit?
Put the inductor back in the junk box. You don't know its value, so it is of no help in finding the value of your capacitor.
Instead, get out some resistors, and set up this circuit:



simulate this circuit &ndash; Schematic created using CircuitLab
C1 is your unknown capacitor.
Try various values of R1 until you get approximately half the voltage on V_C as on V_Siggen.  It needn't be exact - &quot;in the ballpark&quot; is sufficient.  You just don't want 3 V for V_Siggen and 3 millivolts for V_C.
Use the 10X probe on your scope.
Measure the voltages. Peak to peak or RMS, whichever floats your boat.  Just use the same method for both measurements.
With two known voltages and one known impedance, you can apply the voltage divider equations and determine the impedance of the capacitor at the frequency your signal generator produces (1MHz from the question.)
That would be \$ Z_{C1} = \frac {Z_{R1}}{\frac{V_{Siggen}}{V_C} -1} \$
From the impedance and the frequency, you calculate the capacitance as \$C = \frac {1}{2 \pi f Z_C} \$.
All values must be in base units - ohms, farads, volts, hertz.

Keep in mind that capacitors aren't ideal.  If you have an electrolytic capacitor (the kind with aluminum foil in a roll) then it'll probably give you funky values because the rolled up foil will act like an inductor at 1MHz.  There's also other stuff that can cause the results to be off.

If that's too much math and you have a sound card in your PC, then you could download the program described here.
That's a GNU-Radio flow graph that uses the sound card and a series resistor to measure impedances.  It can also measure capacitance and inductance - and resistance, of course.
I put it together to learn about GNU-Radio, but also because this kind of question (how to measure capacitance/inductance/speaker impedance) comes up from time to time here on the EE stack. I thought it'd be nice to have a tool to hand people who don't have a room full of equipment.