.vcxproj in source control

It is the project file for your project. So yes, you'd better check that in. The only file that you might not want to check-in is the .vcxproj.user file. It contains user-specific overrides, particularly debugger settings.

You could only make such a mistake if you are not operating Explorer in "programmer" mode. It has the nasty habit of hiding filename extensions. Fix that with Control Panel + Folder Options, View tab, untick the "Hide extensions for known file types" checkbox.

Of course they need to be added to source control, .vcxproj is the project file. Quoting MSDN:

Project files no longer use the .vcproj file name extension. Visual Studio automatically converts project files that were created by an earlier release of Visual C++ to the format that is used by the current system. For more information about how to manually upgrade a project, see /Upgrade (devenv.exe).

In the current release, the file name extension for a project file is .vcxproj.

The .vcxproj.user files, on the other hand, do not need to be added to source control. The link above describes what each of these files contain as well.