Automatically fire an assignment rule in salesforce using apex trigger

1. trigger AutoAssignmentRuleTrigger on Lead (after insert, after update)
2. {
3.     List<Lead> leadList = new List<Lead>();
4.    
5.     for(Lead currLead : Trigger.New)
6.     {
7.         if((Trigger.isInsert && Trigger.isAfter) && currLead.LeadScore__c != null)
8.         {
9.             leadList.add(new Lead(id = currLead.id));
10.         }
11.         else if((Trigger.isUpdate && Trigger.isAfter) && Trigger.oldMap.get(currLead.Id).LeadScore__c != currLead.LeadScore__c)
12.         {
13.             leadList.add(new Lead(id = currLead.Id));
14.         }
15.     }
16.    
17.     Database.DMLOptions dmo = new Database.DMLOptions();
18.     dmo.assignmentRuleHeader.useDefaultRule = true;
19.     Database.update(leadList, dmo);
20.  
21. }

In the above trigger, default assignment rule has been been initiated by using the below line,

1. dmo.assignmentRuleHeader.useDefaultRule = true;

You can also query the assignment rule and set that rule id in code as below,

1. AssignmentRule AR = [select id from AssignmentRule where SobjectType = 'Lead' and Active = true AND Name = 'Cost Rule' limit 1];
2. Database.DMLOptions dmo = new Database.DMLOptions();
3. dmo.assignmentRuleHeader.assignmentRuleId = AR.Id;
4. Database.update(leadList, dmo);

Reference: 

http://developer.force.com/cookbook/recipe/running-case-assignment-rules-from-apex