How to assign role(s) for a new user based on node_field?
Yes this should be possible using the Rules module.

When trying to do so, make sure to add a Rules condition Entity has field (related to your my_field field). That's also what is mentioned in the Rules UI when you're adding a "data comparison" condition: somewhere it says "The data selector helps you drill down into the data available to Rules. To make entity fields appear in the data selector, you may have to use the condition 'entity has field' (or 'content is of type')".

For a video tutorial that illustrates the importance of this Entity has field condition, refer to Data types and data selection, especially what is shown between about 13:30 and 17:30 in it.