capistrano-strategy-copy-partial is capistrano extension that add strategy for deploy only part (subdirectory) of repository
Add to Gemfile:
gem "capistrano-strategy-copy-partial"
Use next options:
set :deploy_via, :copy_partial
set :copy_partial, "path/for/deploy"
set :copy_strategy, :export
capistrano-strategy-copy-partial is released under the MIT licence: