//Fetching the assignment rules on case
AssignmentRule AR = new AssignmentRule();
AR = [select id from AssignmentRule where SobjectType = 'Case' and Active = true limit 1];

//Creating the DMLOptions for "Assign using active assignment rules" checkbox
Database.DMLOptions dmlOpts = new Database.DMLOptions();
dmlOpts.assignmentRuleHeader.assignmentRuleId= AR.id;

Case newCase = new Case(Status = 'New') ;
//Setting the DMLOption on Case instance
newCase.setOptions(dmlOpts);
insert newCase ;