I use kramdown for markdown parsing and it handles footnotes nicely.

Change this line in your _config.yml file:

markdown: redcarpet

to:

markdown: kramdown

Redcarpet

When you want to use redcarpet there seems to be no convenient solution right now. Although Redcarpet 3 supports footnotes with the syntax you've used, it is not included into Jekyll, because Redcarpet 3 removes Ruby 1.8 compatibility (source).

Solution 1: Use forked Redcarpet 2

See this solution by Jerod Santo:

Add a file called Gemfile to the root of your Jekyll folder with this content:

source "https://rubygems.org"


gem "jekyll"
gem "redcarpet", github: "triplecanopy/redcarpet"

or alternatively djui/redcarpet

Theny adjust your _config.yml to

markdown: redcarpet
redcarpet:
extensions: [footnotes]

Solution 2: Fork Jekyll and include Redcarpet 3

I don't know what's the easiest way to do this. Comments are welcome.

Maruku

似乎支持脚注（source，source）。

As of Jekyll 3.0.0, kramdown is the default Markdown processor, so the example in OP's question now works out of the box. The pattern is:

Some text[^1].


Some other text[^2].


The identifier in the square brackets does not have to be numeric[^my_footnote].


[^1]: Some footnote.
[^2]: Other footnote.


[^my_footnote]: This also works fine.

Update 3rd Jan. 2020:

• GitHub has its own markdown processor GFM, which is an extension of CommonMark. Both kramdown and GFM can be used to render GitHub Flavored Markdown.
• Footnotes are not yet supported by GitHub Flavored Markdown, which means the above examples do not render correctly in the GitHub code repository.
• Kramdown is still the default Markdown renderer for Jekyll. With kramdown, the above examples render correctly on sites based on GitHub Pages.

I found that plugin for jekyll Github orangejulius/jekyll-footnotes. May it solve the issue.

Also I read just today an blog post that Github improves the footnotes.