Use this:

ODP.NET, Managed Driver - Official        

http://www.nuget.org/packages/Oracle.ManagedDataAccess/

This short post is just because most of the information you will find on this topic is out-of-date.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