Editing CSS (style.css) via wp-admin??

Hello all,

I am trying to center my footer text by editing the "style.css" file in Appearance>Editor>style.css.

I put in the code in the css file here:
#footer-links{ text-align: center; }
But the text won't center! It looks like it is calling an entirely different css file. So how can we edit the CSS file within the WP-admin backend?