Unfortunately, the answer by jvperrin didn't help. What we've managed to do is to set the needed log file in initializer:
Delayed::Worker.logger = ActiveSupport::BufferedLogger.new("log/delayed_job.#{Rails.env}.log", Rails.logger.level)
if caller.last =~ /script\/delayed_job/
queues = ARGV.select { |opt| opt =~ /--queue=/ }
queue = /\=(.*)/.match(queues.first) if queues
queue = $1 if queue
if queue
Delayed::Worker.logger = ActiveSupport::BufferedLogger.new("log/delayed_job.#{queue}.#{Rails.env}.log", Rails.logger.level)
end
ActiveRecord::Base.logger = Delayed::Worker.logger
Rails.logger = Delayed::Worker.logger
end