How to add inline css code with background image in page html code?

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cant you just give that link a class? why touch your template files?..
anyhow i see no reason why you can’t to that… the css should work..

The only change i would do when editing a template file is
using php to get the folder url (where you image is) like so:

<style type="text/css">
.specialLink a {
    width: 90%;
    font-family: Helvetica, Arial, sans-serif;
    background: #0e710d url("<?php get_bloginfo('url'); ?>/wp-content/uploads/2012/03/image.png") repeat-x 0 0;
    font-size: 1.6em;
}
</style>

<p class="specialLink"><a href="http://mysite.com/wp-signup.php">Click here &raquo;</a></p>

Again… i reccomend you use your style.css to load that css and not in
template files.. if you need it just for a specific page say so… i have
a better solution for that.

Hope this helps, Sagive.