The phrase "a website that has" is correct and usable in written English.
You can use it when describing the features or content of a specific website.
Example: "I found a website that has a wealth of information on sustainable living practices."
Alternatives: "a site that contains" or "a webpage featuring".
The film has a website that has been providing background information and back stories.
The incursion was reported by a website that has published articles based on leaks from Edward Snowden.
Auction.com is a website that has so far mostly auctioned portfolios of properties in, or close to, foreclosure, on behalf of lenders.
A few months ago they put up a website that has little videos that introduce the icon, but you have to know to go that website.
It handled a million tonnes of cargo a year, and earned at least 30m yuan, according to a website that has been taken down.
Italian-speakers might enjoy Libernazione.it, a website that has an automatic generator of Grillini insults, mostly about banks, subservient media, freemasons and corrupt politicians.
Her office sent out a volley of postcards to young engineers who had scattered around the country, directing them to a website that had a list of job openings and a cost-of-living calculator.
That they did, and we can now say "goodbye" to a website that had only two purposes -- to inform and to protect.
Rachel helped me affix words like "throbbing" and "rippling" to sentences to make them a little sexier and even sent me to a website that had a comprehensive list of reportedly sexy descriptive words for erotic writers to use.
The mainstream media pinpointed the original source of those as 4Chan, a website that had once been full of obsessive Harry Potter fan fiction, but now seemed to be turning on Hermione Granger.
