The best time to visit Rajasthan is from October to February when the weather is pleasant and you can enjoy your trip. This is also the peak season here.
But if you want to avoid crowd then September is the best month as the weather is also pleasant and the views in monsoon months are just breathtaking. You can enjoy the real beauty of this place during this time.
Also, if you wish to visit places like Mount Abu in Rajasthan then do visit it in the summer months as the weather is quite pleasant but say a big no to visiting other places in Rajasthan during summers.