I have a button in my website and I want to send a letter to my arduino
Tat may not be possible. The Arduino isn't serving up the page, is it?
The button is part of a form that has some action associated with it. That action is that some script is run. If the script runs on a server that you don't have physical access to, you won't be able to the connect the USB cable from the Arduino to that server.
If the server is one that you have physical access to, you could connect the Arduino to the server, using the USB cable, and have the action script open the serial port (which will reset the Arduino), wait for the Arduino to be ready, and then send it a message.