No capacitor will not convert directly AC to DC. If you add only a capacitor to an AC circuit, the waveform will remain the same.
The capacitor can be connected across a diode bridge rectifier circuit which will give you a smoother DC signal as only the AC component of the waveform passes through the capacitor and will make the output waveform ripple-free.
Hence, the capacitor converts AC to DC when it is connected to the diode bridge rectifier circuit.