Generating FFT on data recived from 20Amp(ACS712) current sensor using arduino & processing IDE
Yes, it is possible to calculate the FFT directly on the Arduino if the data rate is slow enough, if you don't need full float/double precision and if you don't need an excessive number of bins.

You have not written anything about your data rate, the required precision, or the number of bins, so it's impossible to answer if it's good enough for your needs.

Maybe you can compare your current code with the numbers on ArduinoFFT and figure out if it's good enough.