Is there a website that applies to jobs for you?
Yes, several. Most are browser extensions or bots that fill in application forms in bulk while you do something else. They are cheap and they do what they advertise. Whether that is what you need is a different question.
How auto-apply sites work
You upload one resume, save answers to the common screening questions, and set filters for titles and locations. The tool searches job boards, opens each posting that matches, fills in the form with your saved answers and submits it. Many run as a browser extension inside your own logged-in accounts, and the bigger ones will send hundreds of applications a week.
Pricing usually runs from $99 to $999 a year. For that you get volume and nothing else: nobody reads the postings, and the same resume goes to every one of them.
Where they backfire
One resume for every posting means none of them reads as a fit. Recruiters see generic applications all day and recognize them in seconds.
Screening questions get answered from a template, so you can end up saying yes to a requirement you do not meet, or no to one you do. And applying to the same company several times in one week tells its recruiters exactly how the applications were made.
A tool that drives your own logged-in account can also get that account restricted. LinkedIn, for one, lists bots and browser extensions that automate activity on the site as prohibited software.
When a bot is the right call
If you are going for high-volume roles where speed matters more than fit, such as hourly or entry-level jobs that hire on a rolling basis, casting a wide net fast can be sensible. It is also a cheap way to find out which job titles get any response at all.
It is the wrong tool when the roles are senior, specialized or scarce, because then each application has to look like it was meant for that job.
The other kind of "applies for you"
A reverse recruiter makes the opposite trade: far fewer applications, and a person's judgment on every one. Here that is 5 roles a week, picked by someone who read the posting, each emailed to you first with the reason and where you fall short, with 24 hours to stop it.
Your resume is rewritten for each posting, the application is filed in your name, and you get the confirmation number. It costs $199 a month rather than $99 to $999 a year, and the first 7 days are free.
How to choose
If your applications get interviews but you do not have time to send enough of them, hand the applying to a person. If they do not get interviews, more volume will not help, from a bot or from anyone; the resume or the target needs fixing first.
And if you want to keep applying yourself, just faster, the Resume Tailor builder rewrites your resume for a specific posting in a few minutes.