I am running Tomcat 8.0.30 and to add a version in Tomcat Web Application Manager one can simply rename MyApp (under webapps folder) to MyApp##1.0.2 without creating .war file.
If you want to create .war file, follow these steps:
- Navigate to Tomcat webapps folder, on the address bar type cmd or cmd.exe or else you can open cmd and navigate to your tomcat webapps directory

- Enter this cmd -
jar cvf MyApp.war .
Here MyApp is name of Application, .war is the extension for creating war file (also called as Web Application Archive) and . represents current directory where war file will be created..
After doing this, you'll see MyApp.war file under webapps. Now just rename to MyApp##1.0.2.war and the server will automatically reload the context with name.

That's it!