Yes, it is possible.
You can serve a css file with php by setting the content-type.
<?php header('content-type: text/css; charset=utf-8'); ?>
You would output the css from the php file.
You could store values in a mySQL or other table with a form, and later retrieve them with the mySQLi or other library.
This is an example of the php script:
<?
header('content-type: text/css; charset=utf-8');
$bgColor = "#FFF"; // Get it from database, I'm setting manually for this example
?>
body{
background-color:<?php echo "$bgColor" ?>;
}
Alternatively, you could output inline css on the page. Either directly in to a tag, or inline on elements.
If really needed a native css file for some reason (I can't think of one), you could technically overwrite a specific css file using php's fwrite() function, though I wouldn't recommend doing it this way.
<?php
$filename = "phpstyle.css";
$fp = fopen($filename, 'w');
$bgcolor = "#FFF";
$css = "body{";
$css .= "background-color:".$bgcolor.";";
$css .= "}";
fwrite($fp, $css);
fclose($fp);
?>