Here is a Photoshop tutorial I found on alibony.com on adding pixelated borders to any image. Below I have copied the tutorial from their website and added it here for your benefit. I hope you find this tutorial helpful.
Part 1: Create a Dotted Frame
To create a dotted frame for a photo:
Create a new image with a white background layer:
From the File menu, select New, and then select Blank File.
In the New dialog box, enter the dimensions of your photo and fill the background layer with white.
Create a new Levels adjustment layer above the white background. In the Levels window, do not make any changes and click OK. Notice that the adjustment layer contains a layer mask filled with white. We'll use this layer mask later.
Copy the photo and paste it in the layer directly above the Levels adjustment layer.
With the photo layer active, press Ctrl+G to create a clipping group with the Levels adjustment layer below. The layer mask on the Levels adjustment layer will now be applied to the photo.
Click on the Levels adjustment layer to make the layer mask active:
Using the Rectangular Marquee tool, make a rectangular selection on the photo to create the framed area.
Fill the rectangular selection with black. The photo will now appear to have a white rectangle superimposed on it.
From the Selection menu, select Deselect or press Ctrl+D to deactivate the selection. This is important because you must apply the filter to all pixels in the mask.
From the Filter menu, select Pixelate, then Color Halftone.
In the Color Halftone window, enter a radius of 20px and use the default values for the other settings. (For a different effect, you can change the size of the radius):
Press OK to apply the filter. The image will now look like the following:
With the layer mask still active, from the Filter menu, select Adjustments, then Inverseor press Ctrl+I to invert the black and white colors in the mask. The photo is now framed in white. The Layers palette will look like the following:
Optional: To change the color of the frame, change the color of the background layer.
And here is the picture I made using this tutorial. It took me awhile to get this method down, but once you learn it you will want to use it over and over.