How to Mesure the smoothness of a signal
Hurst exponent is a good option.

For a better answer you must better explain your objective. For example if you are comparing signals and if they have the save length, amplitude, sampling frequency and/or others.

If you are looking for very simple approaches then, for example, you can:


calculate the discrete derivative 
calculate absolute value
sum all values


Another option could be:


apply a low pass filter
calculate difference between original signal and filtered signal
a smaller difference means a smoother signal.