This kind of path is local to the client system. So if I visit a page with this link it will look for your CSS file on my computer, at /home/aib23/public_html/wp-content/themes/striking_r/assets/app_css
Also, you need to use the href attribute in your link element in order for it to work.
I suggest you use a link relative to your web root - like this:
<link rel="stylesheet" href="/wp-content/themes/striking_r/assets/affiliate_app_css/myfile.css" />
Replace myfile.css with the name of your stylesheet.