Yes there is. You can add this to your themes header.
<?php
if(is_home()){
// we are on the home page
echo '<link rel="stylesheet" src="https://wordpress.stackexchange.com/questions/17113/your_stylesheet" />';
}
?>
You can also use other conditional tags to find out if you are on nearly every type of WordPress page. Conditional Tags
Following on from the comments below, this would be better used like this
<?php
if(is_home()){
// we are on the home page
echo '<link rel="stylesheet" src="https://wordpress.stackexchange.com/questions/17113/your_home_stylesheet" />';
}else {
echo '<link rel="stylesheet" src="your_default_stylesheet" />';
}
?>