Open the design you want to give a halftone dot effect.
Create a layer under the original design.
Create a shape that you want to convert into dots.
I copied the outside shape of my design and filled it with black.
You have to enlarge the shape so far that the later created halftone dots are visible below your original design.
My design is round so i can use the scaling option in Illustrator.
If your design has a special shape you have to manually adjust it.
Select Effect > Blur > Gaussian Blur
Use a Radius you want.
The result looks like this.
Select Object > Rasterize…
The resolution should be 600 dpi or more.
Select the object and select Effect > Pixelate > Color Halftone…
The color halftone dialog box will open where you can enter some numbers to adjust the appearance of the effect.
Set a number for the Max. Radius.
This will determine the size of the largest dot in the effect.
The screen angles should be equal.
We need to convert the raster image to vector.
Select the shape and select Object > Live Trace > Make and Expand from the menu.
The shape is now a full vector object.
Select with the Magic wand tool the white area and press delete.
Now we are able to assign the color and set the appearance of the design to overlay with the transparency menu.