Yes, it is possible. The best approach, I would suggest is to have user groups, which can be then used to create User filters at row level while creating the data source.
Creating user filters creates sets with access defined for each set of users (User Groups). This would restrict the access at row level as you will define that which group has access to which data.
These sets, when used as Data Source filter, they restricts the access at row level on the data source.
It works just like active directory, and I have been using it for quite long now.
You can find more details here :Create a User Filter and Secure it for Publishing - Tableau
Hope it helps!!