How to call an Oracle function with a Ref Cursor as Out-parameter from C#?

You sure can. There are a few gotchas to be wary of but here is a test case

create or replace function testodpRefCursor(
                  uniqueId    IN NUMBER 
                 ,resultItems OUT NOCOPY SYS_REFCURSOR) RETURN NUMBER
                 IS

 BEGIN
      OPEN resultItems for select level from dual  connect by level < uniqueId ;
      return 1;
 END testodpRefCursor;

1. I have found that
   functions likes to have the
   ReturnValue as THE FIRST param
   in the collection
2. BindByName is by default FALSE, so it defaults to BIND BY POSITION

Otherwise it is quite straight forward:

  OracleCommand cmd = new OracleCommand("TESTODPREFCURSOR", con);
  cmd.CommandType   = CommandType.StoredProcedure;
  cmd.BindByName = true;
  // Bind 


  OracleParameter oparam = cmd.Parameters.Add("ReturnValue", OracleDbType.Int64);
  oparam.Direction = ParameterDirection.ReturnValue ;       

  OracleParameter oparam0 = cmd.Parameters.Add("uniqueId", OracleDbType.Int64);
  oparam0.Value = 5 ;
  oparam0.Direction = ParameterDirection.Input;

  OracleParameter oparam1 = cmd.Parameters.Add("resultItems", OracleDbType.RefCursor);
  oparam1.Direction = ParameterDirection.Output;




  // Execute command
  OracleDataReader reader;
  try
  {
    reader = cmd.ExecuteReader();

    while(reader.Read() ){
        Console.WriteLine("level: {0}", reader.GetDecimal(0));  
    }

  } ...

Now for more samples go to your Oracle Home directory and look @ the Ref cursor samples in ODP.NET

for instance:
%oracle client home%\odp.net\samples\4\RefCursor

hth