this_is_good.rb

def tag_to_deploy
  Capistrano::CLI.ui.choose do |menu|
    menu.choices *last_ten_tags
    menu.header    = "Available tags"
    menu.prompt    = "Tag to deploy?"
    menu.select_by = :index_or_name
  end
end

def last_ten_tags
  tags = `git tag`.split("\n")
  sorted_tags = tags.sort_by{ |version| version.split('.').map{ |version_level| version_level[/\d+/].to_i } }
  sorted_tags.last(10)
end

this_is_maybe_better.rb

def tag_to_deploy
  Capistrano::CLI.ui.choose do |menu|
    menu.choices *last_ten_tags
    menu.header    = "Available tags"
    menu.prompt    = "Tag to deploy?"
    menu.select_by = :index_or_name
  end
end

def last_ten_tags
  tags = `git tag`.split("\n")
  sorted_tags = tags.sort_by{ |version| version_as_array(version) }
  sorted_tags.last(10)
end

def version_as_array(version)
  version.split('.').map{ |version_level| version_level[/\d+/].to_i }
end

this_is_not.rb

def tag_to_deploy
  require_annotated = /refs\/tags\/(v.+\^\{\})$/
  all_version_tags      = `git ls-remote --tags #{repository}`.scan(require_annotated).flatten
  sorted_version_tags   = all_version_tags.sort_by{|v| v.split('.').map{|nbr| nbr[/\d+/].to_i}}
  stripped_version_tags = sorted_version_tags.map{|tag| tag.strip}
  puts "stripped_version_tags: #{stripped_version_tags.class}"

  last_x_tags = []
  if stripped_version_tags.size > 10
    last_x_tags         = stripped_version_tags[-10..-1]
    puts "last_ten_tags: #{last_x_tags}"
  else
     max = stripped_version_tags.size
     last_x_tags         = stripped_version_tags[-max..-1]
    puts "last_ten_tags: #{last_x_tags}"
  end

  tag = Capistrano::CLI.ui.choose { |menu|
    menu.choices *last_x_tags

    menu.header    = "Available tags"
    menu.prompt    = "Tag to deploy?"
    menu.select_by = :index_or_name
  }
end

I like it, nice refactor. You could break out sorted_tags as well and name it so as to clarify what it is providing:

...
def last_ten_tags
git_tags_sorted_by_version.last(10)
end

def git_tags_sorted_by_version
git tag.split("\n").sort_by{ |version| version_as_array(version) }
end
...

Actually... you might not need version as array - could you do this?

def git_tags_sorted_by_version
  tags.sort_by{ |version| version.gsub(/[^\d]/, '').to_i }
end