cron ignores variables defined in ".bashrc" and ".bash_profile"

You can source the file you want at the top of the script or beginning of the job for the user that is executing the job. The "source" command is a built-in. You'd do the same thing if you made edits to those files to load the changes.

* * * * * source /home/user/.bash_profile; <command>

or

#!/bin/bash
source /home/user/.bash_profile

<commands>

Because it's not an interactive shell. The same happens when you open some terminals.

Have a look at this question: What is the .bashrc file? | Super User

And also at this one:

What's the difference between .bashrc, .bash_profile, and .environment? | Stack Overflow

Different scripts fire depending on if the connection is a login shell (or not), an interactive shell (or not), or both.

If you want to make bashrc you'll need to make this change:

When Bash is started non-interactively, to run a shell script, for example, it looks for the variable BASH_ENV in the environment, expands its value if it appears there, and uses the expanded value as the name of a file to read and execute. Bash behaves as if the following command were executed:

if [ -n "$BASH_ENV" ]; then . "$BASH_ENV"; fi 

but the value of the PATH variable is not used to search for the file name.

As noted above, if a non-interactive shell is invoked with the --login option, Bash attempts to read and execute commands from the login shell startup files.

Source: Bash Startup Files | Bash Reference Manual | gnu.org

You may not be able to run source if the sh shell is being used. This can be changed by adding the following line in your crontab:

SHELL=/bin/bash
* * * * * source "/root/.bashrc"; <command>

You can also specify the environment:

BASH_ENV="/root/.bashrc"
* * * * * <command>

or you can use your local /home/user/.bashrc if it is a user cron job (e.g. crontab -e).

Note that .bash_profile can replace .bashrc, if it exists.

Credit: How to change cron shell (sh to bash)?