How to set the value of a date field via Rules?
Before you will be able to create a Rules Action like "Set a data value" for your date field, you have to make sure to add a Rules condition Entity has field (related to the  field for which you want to set a value). And make sure to add that Entity has field condition BEFORE other Rules Conditions in which you might want to refer to this field.

That's also what is mentioned in the Rules UI, e.g. 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.