ruby is single-threaded, so I assume you are running your rails app on a server like unicorn?
The only solution I can think of is timestamps (with micro seconds) and not using the multi-line Rails log output which is not suitable for anything but single requests in dev environments. But even this does not guarantee "ordered" logs because they can be written when the request was served or at a random time afterwards when the buffer was flushed again.
This is an in-depth tutorial on how to use Log4r that also shows how to get custom timestamps into your logs and have all the important information on a single line. This prevents logs from other requests writing inside your main request and you can have a timestamp resolution of microseconds and order afterwards manually. However the order should not matter if you are running concurrent app-servers because the order is not guaranteed there anyway.