Making a sine wave using a capacitor?

Will be much easier to do with a 555 timer

A 555 will only give you a square or a triangle, any generation of a sine wave will have to be done by wave shaping. This is in effect what Lefty suggested. It is as easy to apply this wave shaping to the output of an Arduino as it would be for a 555.

It depends on what you want to do with the sine wave. For example if you want to energise a coil to make an RFID then simply put in a square wave in at the resonant frequency and it turns into a sine wave.