Yes, the AWS s3 cli [1] has a --sync option that does that.

[1] http://docs.aws.amazon.com/cli/latest/reference/s3/sync.html

Edit: Actually this isn't the dropbox functionality. For that you'd have to wrap it in an inotify loop:

"while true; do inotifywait -r -e modify . && aws s3 sync <local> <s3 bucket>; done"