Air plays an important role in the water cycle indeed.
Firstly, air is a sort of medium in which dust particles propagate through onto which the water particles condense and form clouds. Thus it plays one significant role.
Secondly, the clouds usually form over oceans and other water bodies but only due to the winds which are caused by air, the clouds are able to travel above land and cause rainfall, thus continuing the water cycle.
Hence, air plays an important role.