No, you can't measure it. mAh = milli-Ampere-hours. Thus, to test it, you would have to drain it over time.
Since V = IR, then I = V/R, so you could in theory connect it to some amount of resistance, and see how long it takes to drain. Multiply I*1000*t is the mAh, where t is how many hours it took to die.
For example, a 37Ω resistor on a 3.7v battery, I = 0.1, so a 600 mAh battery would take 0.1amps * 1000 * 6hours to drain.