Is it possible to paste a link without tags and make it directly a link in a post?

I use a similar method to the following in a plugin of mine:

function wpse107488_urls_to_links( $string ) {
    /* make sure there is an http:// on all URLs */
    $string = preg_replace( "/([^\w\/])(www\.[a-z0-9\-]+\.[a-z0-9\-]+)/i", "$1http://$2", $string );
    /* create links */
    $string = preg_replace( "/([\w]+:\/\/[\w-?&;%#~=\.\/\@]+[\w\/])/i", "<a target=\"_blank\" title=\"" . __( 'Visit Site', 'your-textdomain' ) . "\" href=\"$1\">$1</a>", $string);

    return $string;
}

I don’t use it for post content, but it should work there.
For that, you’d have to employ the the_content filter:

add_filter( 'the_content', 'wpse107488_urls_to_links' );

Sidenotes:
This is untested.
The regexes are fairly good, but they will fail in niche cases once in a while. Identifying a URL by format only, while avoiding false positives isn’t the simplest of things.