Converting the value of Vrms to A/sqrt(Hz)
Switch the spectrum analyzer to show the power spectral density (PSD). The display will be normalized to 1Hz bandwidth in \$V/\sqrt{\text{Hz}}\$, which in your case is equivalent to \$A/\sqrt{\text{Hz}}\$

The FFT display you are looking now at is the RMS signal amplitude in each frequency bin. 

It's often a good ideal to familiarize yourself with complex instruments by reading the manual and performing a few simple exercises to understand what it is doing.