The simplest way is probably
using System.IO;
...
File.AppendAllText(originalFilePath, File.ReadAllText(appendFilePath));
[EDIT]
Reading your comments, I wonder what went wrong that it does not work with you. The above appends one text file to an existing one. If the CSV file is not too elaborate (i.e. no multi-line fields, terminates properly on a new-line), then there should not be any format issues (i.e. that all is now in one column(?) as you report). The only thing I could imagine is the character encoding. That's why it was good to see your files (or at least a small and obfuscated portion of it).
[/EDIT]
Cheers
Andi