Can I change header.php of current theme through a plugin function?

If you are looking to insert code into the <head></head> block, then this hook does it:

add_action( 'wp_head', 'wpse_73900_wp_head' );

function wpse_73900_wp_head()
{
    ?>
    <!-- Custom Html --->
    <?php
}

If that’s not the case, then it’s more difficult. I think it would depend on the theme providing a hook at your desired point of insertion.

Another option is to make DOM manipulations with jQuery.

Other quite crazy possibilities can be extracted from this Q&A: Adding onload to body

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