There is an iOS and Android app available called Notate Me that does what you ask. The free version is limited to a single staff but that is often what most of us want for folk tunes anyway.

Notate Me also lets you quickly write down music on your device. It then cleans it up and lets you play it back, print it or whatever. It also imports and exports MusicXML so you can exchange scores with other apps and users.

      - Mark