Might be a duplicate here: How to calculate alcohol without OG reading?
It appears that there is a formula using your Specific Gravity from a hydrometer and if you pick up a refractometer, a measurement from that, that you can use to calculate the ABV. Jump to section "Measurement of ABV" at Brew Your Own for the formula.
From the article:
ABV = [277.8851 - 277.4(SG) + 0.9956(Brix) + 0.00523(Brix2) + 0.000013(Brix3)] x (SG/0.79)
In this equation, Brix is the Brix reading of your refractometer and SG is the specific gravity reading from your hydrometer.
If you try this, it is important to take very careful readings. Degas the sample in a blender or by pouring it between two glasses until it does not foam. Make your reading at as close to 68 °F (20 °C) as possible. If your hydrometer is calibrated in Brix, use the longer formula I cited earlier to convert it to SG. This equation fits very well with the data points. Measure-ment of ABV can be made to within 0.3% if you are careful.