If you specifically want an app on your phone, the field is small: a dedicated handwriting app, and the free tools built into Android and iOS. They are convenient for capturing a note on the spot, and limited in the ways phone tools usually are, with no batch processing and weaker results on cursive.
One thing worth knowing before you commit to an app: the most accurate handwriting OCR is generally web and API based, not an app. If accuracy on cursive or volume matters more than phone convenience, a specialist website will beat any of the apps here. For tidy notes on the go, though, an app is the right shape.