Note: Travis CI does not yet provide rebar3 as a build tool for Erlang projects, so you will have to include a rebar3 executable escript in your repository.

In your application's .app.src file use "git" as the version. This will replace the version string with the current tag when publishing the hex package:

{vsn,"git"},

In the .travis.yml configuration add the below section so that the script scripts/hex.sh is run everytime a new tag is made:

deploy:  
  provider: script
  script: scripts/hex.sh
  on:
    tags: true

Create the script hex.sh under scripts/ and make it executable:

#!/usr/bin/env bash

## Setup hex user
mkdir -p ~/.hex  
echo '{username,<<"'${HEX_USERNAME}'">>}.' > ~/.hex/hex.config  
echo '{key,<<"'${HEX_KEY}'">>}.' >> ~/.hex/hex.config

## Add the rebar3 hex plugin to global
mkdir -p ~/.config/rebar3  
echo '{plugins, [rebar3_hex]}.' > ~/.config/rebar3/rebar.config

./rebar3 hex publish <<EOF
y  
EOF  

In the script it relies on two environmental variables $HEX_USERNAME and $HEX_KEY. Using either the Travis CLI tool or web interface you can create these variables and have the values encrypted or unseen by viewers of your repository. For instructions see the Travis-CI environment variables docs.