Use this:

Oracle Data Provider for .NET (ODP.NET) Managed Driver

http://www.nuget.org/packages/odp.net.managed

This short post is just because most of the information you will find on this topic is out-of-date.

Oracle finally wrote a 100% managed code ADO.NET provider and it's available on NuGet.  So you can just right-click on your references and grab the NuGet package.  Not install, no bitness headaches.

David