Build a complete HTML page in the opened window and reference your CSS-file there:
var win = window.open('','printwindow');
win.document.write('<html><head><title>Print it!</title><link rel="stylesheet" type="text/css" href="https://stackoverflow.com/questions/18758288/styles.css"></head><body>');
win.document.write($("#content").html());
win.document.write('</body></html>');
win.print();
win.close();