I am not familiar with the EGit plugin, but do you have the option to import it as a Java project? The "Add Scala Nature" option is available only for Java projects.
If you cannot create it as a Java project, you can also just modify the generated .project file and add the Java character to it:
<nature>org.eclipse.jdt.core.javanature</nature>
(taken from http://enarion.net/programming/eclipse-change-general-to-java-project/ )
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