Yes, almost certainly. If you are not collecting personal data you might not need one but visitors expect to see a policy. You can just state this in your privacy policy. Sundial can provide a simple privacy policy but you may prefer to get legal advice as it’s a complex area on some websites.
https://www.termsfeed.com/blog/privacy-policy-no-data-collected/
This article explains it well although I think it’s a grey area that you don’t need one if you don’t process personal data. Are you sure you are not collecting analytics, storing cookies, capturing IP addresses?
https://harperjames.co.uk/article/what-is-a-privacy-policy/
GDPR law states you must have an active opt-in/out for cookies on your website also. That’s a very quick job and Sundial can add that in (check the one on this website) – just contact me.