Вот так можно:

FileStream sourceFile = File.OpenRead(@"C:\zip.xml");
FileStream destFile = File.Create(@"C:\zip.zip");

GZipStream compStream = new GZipStream(destFile, CompressionMode.Compress);

try
{
    int value = sourceFile.ReadByte();
        while (value!= -1)
        {
            compStream.WriteByte((byte)value);
                value = sourceFile.ReadByte();
        }
}
finally
{
    compStream.Dispose();
}