Next, you either just create a fresh content on your site and replace the dead link in Wikipedia with your content.
Or you can search for sites which are linked to the dead page. You then contact them and ask them to replace the dead link with the link to your site.
Here are the details on how to do it:
Step One: Find Dead Links or Broken Links in Wikipedia
1. Go to Google and type this in the search box: site:wikipedia.org [keyword] + “dead link”. Press Enter key.
3. To find the phrase “dead link” on the page, press ctrl + f. A horizontal band together with an empty box will pop up at the bottom of the Wikipedia page.
4. Type the phrase dead link in the empty box and press Enter key. Immediately it will jump to the References section where the phrase "dead link".
i) Go to this free tool called Wikigrabber.
Type in the keywords to search for the dead links.
ii) Here is the link where you can all articles with dead external links of Wikipedia. http://en.wikipedia.org/wiki/Category:All_articles_with_dead_external_links
Step Two: How To Get Backlinks From Wikipedia
There are two methods to get backlinks from Wikipedia.
i) Directly from the dead links in Wikipedia
ii) From sites linking to those dead links.
First Method: Create New Content On Your Site And Link It To The Dead Link In Wikipedia
After you have created a fresh content on your blog or website, you go to the Wikipedia entry and click the “edit” button on the top right.
First you must create a user account with Wikipedia, then only you can edit it.
Before you add link to that particular dead link, make sure you edit other articles first.
Second Method: Get Links (Do Follow) From Sites Linking To The Dead Link
Paste the URL of that broken link into this link analysis tool called Ahref.
From here you can see a list of sites that are linking to the dead page.
Then you can contact them and ask them to replace the dead link with the link to your site.
That's how you can get back-links from those dead links from Wikipedia.