No, no need for a spectrum analyser (and there are plenty of distortion meter projects on the net) - basically you need a VERY low distortion sine wave oscillator to start with, and a VERY sharp notch filter at that frequency, followed by an AC millivoltmeter.
The OPA2134 has distortion as low as 0.00008% which is so low that you cannot measure it.
Here is a website where very expensive equipment is used past its limit (0.0005%) for opamp distortion measurements. All the common audio opamps are measured: **broken link removed**