Here is what you will want to do:
1. Tap your score where you would like to split a measure so that the green status bar is in the desired location. You can then tap the single bar line to enter a bar line in that location. The single bar line is in the 3rd pane from the right in the palette.
2. Tap and hold your finger on the new bar line until you see a menu appear. Select "Make Pickup Bar" or "Make Partial Bar."