Yes, two ways:
1. Open the Notes app. It will show in the Dock on the right-hand side near the Trash can icon. Click and hold or right-click/Option-click on the Notes icon in the Dock, then select Keep in Dock from the Options menu that pops up.
2. Open your Applications folder, find the Notes app icon, click and hold on it, then drag it to the Dock. Navigate to where you want to put it on the Dock while still holding the button down and the two icons will slightly spread apart where you have dragged it to, then release. It should then stay in the Dock.
C