As far as I know, there is no default way to do this via Import/Export. You can do it manually for each category going to
Catalog -> Categories -> Manage categories -> Category products - position from to.
In case you have some tech knowledge, you can use use script to perform it.
If you consider extension, you can try Store Manager for Magento app to bulk set positions of products in category via import. You need 3 columns: SKU, category path and position. Here is tutorial of how it works -
https://www.mag-manager.com/useful-articles/tipstricks/sort-magento-products-within-a-category/
The app is paid, but if the task is one-time procedure you can use 2-week free version from the link in my signature (no cc or paypal required).