Sure thing. You can either start a new functions.php in your child theme (be sure to start it with a
<?php line before adding in anything else.
Alternatively, you can use a core functionality plugin.
The idea of this is that it is a custom plugin that you can dump everything you want into it, like functions.php, but it'll stay with you through theme changes or updates.
An example of one is at https://github.com/billerickson/Core-Functionality
In Bill's case (the author of the one above), he has a good amount of structure to his. You can make one just as simple as a "my-core-functions.php" file that you place in your /wp-content/plugins folder. As long as it starts with something like this, it'll show in your Plugins list and you can activate/deactivate like other plugins.
Since this is a new php file, it does need to start with the <?php in the link above. After that "header" information, you can drop in code there instead of functions.php