I am getting this error while on of my .Net
application are trying to make a connection to oracle database.
The error says that This problem will
As it was pointed out in the comments, System.Data.OracleClient is deprecated. There is little reason to start using it so late in the game.
Also as pointed out in the comments (I've marked this as community wiki in observence), there is now a managed provider as part of the 12c and later versions of the odp.net package. This provider does NOT require any unmanaged dlls so this should be a non issue in that case.
If you would prefer to use the old unmanaged Oracle.DataAccess provider from oracle, the simplest solution is to set the "DllPath" configuration variable:
See "Search Order for Unmanaged DLLs" in http://docs.oracle.com/database/121/ODPNT/InstallODP.htm for more information