One prayer that some people use as a meditation technique is the Jesus Prayer: "Lord Jesus Christ / Son of God / Have mercy on me / a sinner." (Some drop the "a sinner" part.) They recite (out loud or mentally) the first bit while breathing in ("Lord Jesus Christ, Son of God") and then recite the second bit while exhaling ("have mercy on me").

I think that as a technique for managing worry, this works best with something short and easy to memorize and recall, but YMMV.