just google relevant keywords https://www.google.com/search?q=accessibility+scan+website
and if you want the full experience: just enable the screen reader and try to use your website with it.
/edit: and i almost forgot: chromes build-in Audit tool in the Developer Panel includes some Accessibility tests as well
Screen readers often cost significant amounts of money, and are not trivial to "just turn on".
* WAVE (Chrome or FF plugin, https://wave.webaim.org/extension/)
* AXE (https://www.deque.com/axe/)
* AChecker (https://achecker.us/checker/index.php)
* Funkify (Chrome plugin, tries to emulate various disabilities)
* Lighthouse in Chrome Dev Tools also checks some accessibility rules
The full list of things that you need to take care of: https://www.w3.org/TR/WCAG21/ (it's huge I know, it takes 5-7 days to test everything from this list)
My team at Microsoft recently open sourced a tool called Accessibility Insights (https://accessibilityinsights.io). The web version is a chromium extension that includes both automated scans and also a guided assessment option that leads you through how to test for and fix the stuff that has to be found manually. This is the tool Microsoft pushes its own teams to use as part of their release processes.
First, can you navigate your entire site without using a mouse (including any widgets, forms, embeded stuff)? You should also have a "Skip to main content" button that is the first element you hit when you tab into your page.
Next, download the NVDA screen reader, which is free, turn off your monitor (or close your eyes), and navigate your site using it. I recommend using FireFox for this.
Finally, use a color contrast analyzer plugin for your browser to ensure you have enough contrast between all of you elements.
From there, you can review the WCAG 2.0 spec to get into the fine details. If you have the budget, hire a consultant/contractor. What I described above doesn't make your site pleasent to use for a disable person, just usable.
It's also always place this field after the Submit button with the idea that a user with a screen reader would never make it that far. Bots still see it and add it to the post request since I don't think they care about the order of the form fields.
An element that is not displayed should not be 'displayed' by screen-readers either.