The speed of the motor does not matter that much. However, if the motor is too fast it will create mechanical resonances during or at the end of the measurement which will be visible in the results. Most important is that the motor speed and your VNA settings are matched. The most accurate synchronization is a pulse via the motor amplifier or controller set connected to the VNA and then with software the setting after how many pulses the VNA should get a trigger. The trigger can then be related to whatever resolution (degree).

Another less accurate option is to estimate the rotational time of the positioner. Set the VNA to continuous wave mode and set the sweep time similar to the rotational time of the positioner. Set the number of points to what ever you want related to the resolution (degree). This will give you an indication and a possible accuracy of approx. a degree.

What is not taken into account is the start and stop movement which are normally not linear. Good luck.

Acutuall I was thinking if we want to measure radiation pattern of  a single frequency, first in Azimuth and then in Elevation. How much speed should we set so that we get minimum time for the measurement. I would measure each sample after 5 degrees.

Can we set the speed at 5 deg/5sec? so that total measured time to calculate azimuth pattern be 6 mins?

Why would you set your speed to 5 deg / 5 sec? Why not 1 deg / 1 sec? What do you expect what the effects are? In other words what is your question.

Look at this movie close to the end. It is at mm-wave range but the same accounts for lower frequencies. It is CW for both E- and H-plane of a patch antenna. The movie is accelerated but one scan takes approx. 1.30min for 180 degrees. This related to the setting of the IF BW or averaging.

https://www.youtube.com/watch?v=25ky8smtuGc

I assume you have calculated the number of samples based on the width of the target and the frequency of the measurement, so that the difference in change in range between the two sides of the target is not more than half a wavelength per sample (if you are using coherent data).

There is no minimum RPM.  You can use 0.00000001 RPM if you like, but your measurement will take a very long time.

There is a maximum RPM though.  This is determined by the sensitivity of the radar system as a function of measurement bandwidth, and the RCS you want to measure.  You may wish to measure in 1 Hz bandwidth to get good signal-to-noise-ratio, in which case you can only take one (IQ, Cos Sin, real imaginary) sample per second.  Then at 120 samples per revolution the maximum rotation rate will be 0.5 RPM.

The slower you go the more sensitive the system will be, assuming that you have a filter narrow enough to match your sample rate.  With narrow enough filters and slow enough rotation eventually the RCS of the measurement environment will be significantly bigger than the system noise and it is not worth having any extra sensitivity.

The question is very simple. I want to measure E-plane radation pattern and H-plane radiation pattern. I will place the antenna on a rotating table on antenna in the anechoic chamber. I will rotate the antenna first in azimuth and than in elevation to get the rad pattern measurement. What speed should i set of the motor to get like 120 points on my polar graph?

Sorry - I didn't read the question properly, and answered as if you were measuring RCS.

The rotation speed depends on the sample rate of the VNA, and this depends on the filter bandwidth you choose.  You will need to narrow the VNA filter bandwidth until the noise floor is well below the measured signal for all the polar diagram you wish to measure accurately.  This will give you a sample rate.  The narrower the bandwidth the slower the sample rate and the further you will be able to see down the polar diagram.  You need to set the rotation rate of the turntable so that 120 samples at the resulting sample rate fit in one revolution.  You may be able to synchronise the two, or trigger sampling of the VNA from the turntable, making sure that it remains at least as slow as the rate set by the filter bandwidth.  Getting the samples to fall exactly every 3 degrees can be challenging with some equipment combinations, as the necessary output trigger or input trigger may not be available, so you may have to rely on setting the rotation rate to be as close to a multiple of 120 samples per turn as you can and letting it free run, or taking samples very fast (or running the turntable very slowly) and using markers at 0 and 360 degrees for example to select the samples that are very close to the 3 degree steps you need.