No, you can't play Netgammon on your Android phone, because there is no version for this operating system. However, since there are other alternatives, I recommend you check them.
For example, Backgammon Live Online is a game that supports online playing of Backgammon: https://play.google.com/store/apps/details?id=com.lirina.backgammonlive
Use the link above to access its application page at Play Store. Click Read More on the page to check its full description.
