Use the -p flag and add /udp
suffix to the port number.
-p 53160:53160/udp
Full command
sudo docker run -p 53160:53160 \
-p 53160:53160/udp -p 58846:58846 \
-p 8112:8112 -t -i aostanin/deluge /start.sh
If you're running boot2docker on Mac, be sure to forward the same ports on boot2docker to your local machine.
You can also document that your container needs to receive UDP using EXPOSE in The Dockerfile
(EXPOSE does not publish the port):
EXPOSE 8285/udp
Here is a link with more Docker Networking info covered in the container docs: https://docs.docker.com/config/containers/container-networking/ (Courtesy of Old Pro in the comments)