How can I record RF?
If your goal is to generate the plot shown in your question, the JRE is correct, you would use a spectrum analyzer (SA). In fact, with a spectrum analyzer, the data you'd get would be essentially the plot you showed, and you wouldn't need to do any post-processing to get it.

But, you'll notice that the plot doesn't show any phase information about the signal at different frequencies. And an SA does not typically store phase information. So if there is other processing you want to do that requires the phase information, or requires reconstructing the time-domain waveform of the signal you measured, then an SA will not do what you want. 

You can buy a digital storage oscilloscope with bandwidth up to over 100 GHz (and sampling rate over 250 GHz). This would allow you to do what you specifically asked for, Take the FFT of the data to get a spectrogram, and to do it for signals up to ~100 GHz. However you must be prepared to spend quite a lot of money to get this capability. AFAIK these scopes retail in the ~$1 million range at the high end.