I have a program that I need to create a DLL for, hopefully in C#. The program is written in Delphi and I have an interface file to code to. The interface uses the stdcall
This is not directly possible. C# is managed code. This means that it requires a very specific runtime environment in order to function, an environment which Delphi could not directly provide to it. It is not like C where you simply find the address and calling convention of the function and call it.
However, it is possible to host the Common Language Runtime inside of a Delphi application (or any other Windows application). I have no idea how to do this. I just know that it's possible. (It's quite likely that's what this 'Hydra' that Steve mentioned will do.)