It's not clear if you have the Twitter handle and are looking for the website in the profile, or have the website and are looking for the twitter handle.
If you have the website, you can use a search engine and get some results: "timewise.how" site:twitter.com
If you have the twitter handle, you can use the API to get a user object that contains the website url.
For further actions, you may consider blocking this person and/or reporting abuse
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It's not clear if you have the Twitter handle and are looking for the website in the profile, or have the website and are looking for the twitter handle.
If you have the website, you can use a search engine and get some results:
"timewise.how" site:twitter.com
If you have the twitter handle, you can use the API to get a user object that contains the website url.