Create a new square dimension file (ie. 800 x 800px). Make a spectrum gradation in the middle of the document using the Gradient tool with the default “Spectrum” preset. Go to Filter > Distort > Polar Coordinates. There you go, a perfect circle spectrum!
Now, you have to blur the sharp edge. Go to Filter > Blur > Gaussian Blur, apply 5 to 10px radius, depending on the size of your document. Bigger document size will require more blur.
If you only to show partial of the rainbow, you can use the layer mask to hide the unwanted area. In the Layer palette, click on the “Add layer mask” icon. Use Gradient tool, select the “black to transparent” swatch, drag from left to right to mask out the unwanted area.