You may try something like that:
public Stream ConvertToBase64(Stream stream)
{
Byte[] inArray = new Byte[(int)stream.Length];
Char[] outArray = new Char[(int)(stream.Length * 1.34)];
stream.Read(inArray, 0, (int)stream.Length);
Convert.ToBase64CharArray(inArray, 0, inArray.Length, outArray, 0);
return new MemoryStream(Encoding.UTF8.GetBytes(outArray));
}