You can get close with a Cognito Identity Pool that exchanges your user's keys for AWS credentials associated with an IAM role that has access to the resources you want to read/write on their behalf. Pretty standard pattern.

https://docs.aws.amazon.com/cognito/latest/developerguide/co...

edit: I think I misread your comment. I understood it as your app wanting to delegate access to a user's data to the client, but it seems like you want the user to delegate access to their own data to your app? Different use-cases.