Yes. It's an easy task for a cron job, but you have to give more details. For example, do you want to zip (or gzip) all the files in that directory or do you need to select some of them based on some criteria (file name, last modification time and so on)? What have you tried so far?
When you have written the script, make it executable and edit the crontab to schedule the job at some specific time of the day or at some day of the month or at some day of the week. Look at
for details about the crontab format. Due to some limitations of the cron environment, it is a good practice to use absolute path for all the commands within the script and to change directory whenever you have to do some actions from a specific location.