How to run a script only once per day with cron without specifying execution time

Solution 1:

You may want to use the anacron.

From its man page

NAME
       anacron - runs commands periodically

SYNOPSIS
       anacron [-s] [-f] [-n] [-d] [-q] [-t anacrontab] [-S spooldir] [job] ...
       anacron [-S spooldir] -u [-t anacrontab] [job] ...
       anacron [-V|-h]
       anacron -T [-t anacrontab]

DESCRIPTION
       Anacron  can  be  used  to  execute  commands periodically, with a frequency specified in days.  Unlike
       cron(8), it does not assume that the machine is  running  continuously.   Hence,  it  can  be  used  on
       machines  that  aren't running 24 hours a day, to control daily, weekly, and monthly jobs that are usu‐
       ally controlled by cron.

The Ubuntu community HowTo: https://help.ubuntu.com/community/CronHowto

Using anacron:

1. Simply put the executable script file in the /etc/cron.hourly, /etc/cron.daily, /etc/cron.weekly or /etc/cron.monthly.

2. Touch the script file:

   sudo touch /etc/cron.daily/scriptfile
   

   (cron.daily if it is a daily job).

Testing anacron:

sudo anacron -f -d

   -f     Force execution of the jobs, ignoring the timestamps.
   -d     Don’t fork to the background.  In this mode, Anacron will output
          informational  messages to standard error, as well as to syslog.
          The output of jobs is mailed as usual.

Anacron messages in the log:

grep anacron /var/log/syslog

Anacron keeps timestamps in the /var/spool/anacron/. If you remove cron.daily, cron.weekly or cron.monthly files from there, anacron will execute daily, weekly or monthly scripts at the next startup.