Yes it is possible.
You need to use the getDeclaredField method (instead of the getField method), with the name of your private field:
Field privateField = Test.class.getDeclaredField("str");
Additionally, you need to set this Field to be accessible, if you want to access a private field:
privateField.setAccessible(true);
Once that's done, you can use the get method on the Field instance, to access the value of the str field.