Like @svn said the Info.plist
states which orientations your application support. This can be further customized (e.g. restricted) by overriding GetSupportedInterfaceOrientations
.
But there's also (new in iOS 6) PreferredInterfaceOrientationForPresentation which can (and should be) overridden.
More details, including iOS6 specific features, are available in Apple documentation.
I also tried to set the deployment target to iOS6, but I can only switch up to 5.1 in the drop down list.
That sounds like the Xcode you're using does not have the 6.0 SDK. See my comment on your question on how you can check what's being used by MonoDevelop to build your application.