Before you can center it, first you must know how big it is.  This can be accomplished with the GetWindowRect() API.  After that it's simply a matter of calculating the center position taking into account the size of the screen:
public partial class Form1 : Form
{
    [DllImport("user32.dll")]
    [return: MarshalAs(UnmanagedType.Bool)]
    static extern bool GetWindowRect(IntPtr hWnd, out RECT lpRect);
    [StructLayout(LayoutKind.Sequential)]
    public struct RECT
    {
        public int Left;        // x position of upper-left corner
        public int Top;         // y position of upper-left corner
        public int Right;       // x position of lower-right corner
        public int Bottom;      // y position of lower-right corner
    }
    private const int SWP_NOSIZE = 0x0001;
    private const int SWP_NOZORDER = 0x0004;
    private const int SWP_SHOWWINDOW = 0x0040;
    [DllImport("user32.dll", SetLastError=true)]
    static extern bool SetWindowPos(IntPtr hWnd, IntPtr hWndInsertAfter, int X, int Y, int cx, int cy, int uFlags);
    Process process;
    public Form1()
    {
        InitializeComponent();
        process = Process.GetProcessesByName("calc").FirstOrDefault();
    }
    private void button1_Click(object sender, EventArgs e)
    {
        if (process == null)
            return;
        IntPtr handle = process.MainWindowHandle;
        if (handle != IntPtr.Zero)
        {
            RECT rct;
            GetWindowRect(handle, out rct);
            Rectangle screen = Screen.FromHandle(handle).Bounds;
            Point pt = new Point(screen.Left + screen.Width / 2 - (rct.Right - rct.Left) / 2, screen.Top + screen.Height / 2 - (rct.Bottom - rct.Top) / 2);
            SetWindowPos(handle, IntPtr.Zero, pt.X, pt.Y, 0, 0, SWP_NOZORDER | SWP_NOSIZE | SWP_SHOWWINDOW);
        }
    }
}