Is there any AWS service that is able to log URL query string?

This is an interesting question that highly depends on the application that you are aiming to deploy.

There are ways to achieve query string logging in CloudFront (https://medium.com/@stefdaems/aws-cloudfront-with-query-parameters-4b5a2ee171ad), maybe even out of the box if you configure it correctly. The application load balancer (https://docs.aws.amazon.com/elasticloadbalancing/latest/application/application-load-balancers.html) should support it natively.

Regards Johannes