The rainbow as a sign of covenant in the Bible:
In Genisis 9, God places a rainbow in the clouds as a sign of an everlasting covenant between God and man:
13I do set my bow in the cloud, and it shall be for a token of a covenant between me and the earth. 14And it shall come to pass, when I bring a cloud over the earth, that the bow shall be seen in the cloud: 15And I will remember my covenant, which is between me and you and every living creature of all flesh; and the waters shall no more become a flood to destroy all flesh. 16And the bow shall be in the cloud; and I will look upon it, that I may remember the everlasting covenant between God and every living creature of all flesh that is upon the earth. 17And God said unto Noah, This is the token of the covenant, which I have established between me and all flesh that is upon the earth. (King James Bible)
The Hebrew words " בקשתי בענן " or "qesheth `anan" translate literally to "bow of me in the clouds."
See more about the rainbow colors of faith.