How to set cronjob with non-root user?

Yes you can run its own, cron in specific user without sudo, As each user will be having the crontab file no need to install it explicitly. to run crontab of any user, use -u option , please note that user must be privileged to use -u

 $ crontab -u  -e

/etc/crontab is the system wide crontab.

The format of /etc/crontab is like this:

# m h dom mon dow user      command
*   *  *   *   *  someuser  echo 'foo'

while crontab -e is per user, it's worth mentioning with no -u argument the crontab command goes to the current users crontab. You can do crontab -e -u to edit a specific users crontab.

Notice in a per user crontab there is no 'user' field.

# m h  dom mon dow  command
*   *   *   *   *   echo 'foo'

An aspect of crontabs that may be confusing is that root also has its own crontab. e.g. crontab -e -u root will not edit /etc/crontab

See Configuring cron for more information: https://www.freebsd.org/doc/handbook/configtuning-cron.html

In most Linux distros, per user crontabs are typically stored in: /var/spool/cron/crontabs/