请试试这个：

func handler(granted: Bool, error: NSError!) {
    // put your handler code here
}

@IBAction func click(sender: AnyObject) {
    let eventStore = EKEventStore()

    // 'EKEntityTypeReminder' or 'EKEntityTypeEvent'
    eventStore.requestAccessToEntityType(EKEntityTypeEvent, completion: handler) 
}

另一个变体是：

@IBAction func click(sender: AnyObject) {
    let eventStore = EKEventStore()

    // 'EKEntityTypeReminder' or 'EKEntityTypeEvent'
    eventStore.requestAccessToEntityType(EKEntityTypeEvent, completion: {
        granted, error in

        // put your handler code here
        })
}