No. A rainbow is a direction, not a thing. It forms a circle around the opposite direction to the sun -- you'll notice the shadow of your head is always in the middle, and it appears to move with you, as the sun does. It's the effect of the sun refracting through millions of spherical droplets of water.
A full rainbow is a circle, but there is not usually enough rain or spray to see the bit close to you against the ground. Usually that part fades out. That's why the most spectacular ones are when the sun is low -- more of the circle is then up against the sky.
The whole circle can sometimes be seen when looking down on waterfalls, on clouds from a plane or mountain, or in sunlit spray on the motorway. Occasionally you can see individual sunlit dewdrops refracting bright colours in the same way.
Try experimenting with a fine hose spray on a sunny day and you'll see how it works.