Is it possible to Turn page programmatically in UIPageViewController?

Yes it is possible with the method:

- (void)setViewControllers:(NSArray *)viewControllers 
                 direction:(UIPageViewControllerNavigationDirection)direction 
                  animated:(BOOL)animated 
                completion:(void (^)(BOOL finished))completion;`

That is the same method used for setting up the first view controller on the page. Similar, you can use it to go to other pages.

Wonder why viewControllers is an array, and not a single view controller?

That's because a page view controller could have a "spine" (like in iBooks), displaying 2 pages of content at a time. If you display 1 page of content at a time, then just pass in a 1-element array.

An example in Swift:

pageContainer.setViewControllers([displayThisViewController], direction: .Forward, animated: true, completion: nil)

Since I needed this as well, I'll go into more detail on how to do this.

Note: I assume you used the standard template form for generating your UIPageViewController structure - which has both the modelViewController and dataViewController created when you invoke it. If you don't understand what I wrote - go back and create a new project that uses the UIPageViewController as it's basis. You'll understand then.

So, needing to flip to a particular page involves setting up the various pieces of the method listed above. For this exercise, I'm assuming that it's a landscape view with two views showing. Also, I implemented this as an IBAction so that it could be done from a button press or what not - it's just as easy to make it selector call and pass in the items needed.

So, for this example you need the two view controllers that will be displayed - and optionally, whether you're going forward in the book or backwards.

Note that I merely hard-coded where to go to pages 4 & 5 and use a forward slip. From here you can see that all you need to do is pass in the variables that will help you get these items...

-(IBAction) flipToPage:(id)sender {

    // Grab the viewControllers at position 4 & 5 - note, your model is responsible for providing these.  
    // Technically, you could have them pre-made and passed in as an array containing the two items...

    DataViewController *firstViewController = [self.modelController viewControllerAtIndex:4 storyboard:self.storyboard];
    DataViewController *secondViewController = [self.modelController viewControllerAtIndex:5 storyboard:self.storyboard];

    //  Set up the array that holds these guys...

    NSArray *viewControllers = nil;

    viewControllers = [NSArray arrayWithObjects:firstViewController, secondViewController, nil];

    //  Now, tell the pageViewContoller to accept these guys and do the forward turn of the page.
    //  Again, forward is subjective - you could go backward.  Animation is optional but it's 
    //  a nice effect for your audience.

      [self.pageViewController setViewControllers:viewControllers direction:UIPageViewControllerNavigationDirectionForward animated:YES completion:NULL];

    //  Voila' - c'est fin!  

}