Is there a way people can download a mobile application directly by clicking on a URL link?

You’re confusing web sites and apps. Apps have to be downloaded on to the mobile device from an app store.

1)
On Android you can link to the Google Play Store.

Look on that page for “Show the store listing for a specific app”.

2)
Android has a new feature called Instant Apps.They run in the browser without installing.
How to Use Instant Apps

3)
For iOs there is Link Maker
Create links for Apple Music, the iTunes Store, the App Store, the iBooks Store, and the Mac App Store.

I know those don’t exactly answer the question, they require another step beyond merely clicking.

You can make a link that opens the app store to your app’s page, or you can upload the APK or IPA file to the internet and directly link to it, but I would recommend the former. People are annoyed (and rightly so) when a link unexpectedly causes a download. They want to consent to downloading apps.

@ Mariah – thank you

You mentioned “you can upload the APK or IPA file to the internet and directly link to it”.

Could you please explain how this works? You are saying we can create a link that directly prompts the APK/IPA file to download onto our phone?

Find any file hosting site and upload the APK/IPA file to it, sure. The user would still have to install the app from the downloaded file, which I’m sure they would not do.