http://elixir-lang.org/getting_started/1.html を参照 
まずは erlang-r16 が必要なのでそれを入れる
$ brew tap homebrew/versions # untap で戻すらしい
$ brew install erlang-r16
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==> Compilation takes a long time; use `brew install -v erlang` to see progress
==> ./otp_build autoconf
==> ./configure --prefix=/usr/local/Cellar/erlang-r16/R16B --enable-kernel-poll --enable-threads --enable-dynamic-ssl-lib --enable-shared-zlib --enable-smp-support --with-dynamic-trace=dtrace --enable-hipe --enable-darwin-64bit
==> make
==> make install
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Warning: Could not link erlang-r16. Unlinking...
Error: The `brew link` step did not complete successfully
The formula built, but is not symlinked into /usr/local
You can try again using `brew link erlang-r16'
なんかエラー出た。言ってる通り brew link を打ってみる。
$ brew link erlang-r16
Linking /usr/local/Cellar/erlang-r16/R16B... Warning: Could not link erlang-r16. Unlinking...

Error: Could not symlink file: /usr/local/Cellar/erlang-r16/R16B/bin/typer
Target /usr/local/bin/typer already exists. You may need to delete it.
To force the link and delete this file, do:
  brew link --overwrite formula_name

To list all files that would be deleted:
  brew link --overwrite --dry-run formula_name
今度は --overwrite しろと言われたのでそのとおりやってみる
$ brew link --overwrite erlang-r16
Linking /usr/local/Cellar/erlang-r16/R16B... 5417 symlinks created
入ったっぽい。

elixir を入れる
$ brew install elixir
==> Downloading https://github.com/elixir-lang/elixir/tarball/v0.7.1
Already downloaded: /Library/Caches/Homebrew/elixir-0.7.1.tgz
==> make
==> elixir (compile)
ERROR: OTP release R16B01 does not match required regex R15
make: *** [erlang] Error 1

アレ。0.9.3 最新らしいのにすごい古いな。update
$ brew update
$ brew info elixir
elixir: stable 0.9.3, HEAD
Not installed
From: https://github.com/mxcl/homebrew/commits/master/Library/Formula/elixir.rb
よし、0.9.3 が出て来たのでもう1回
$ brew install elixir
=> Downloading https://github.com/elixir-lang/elixir/archive/v0.9.3.tar.gz
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==> make
ἷA  /usr/local/Cellar/elixir/0.9.3: 273 files, 3.2M, built in 89 seconds

interactive elixir shell を起動して確認
$ iex
iex(1)> 1 + 1
2