Thanks for the solution markob83, but I can't get it to work.
I downloaded the following files :
http://code.jquery.com/ui/1.10.3/themes/smoothness/jquery-ui.css
http://code.jquery.com/jquery-1.9.1.js
http://code.jquery.com/ui/1.10.3/jquery-ui.js
I uploaded the js files to the location all my other js files are saved, and did the same with the css file.
I then added the code you provided to my header file, and created a new text field, and assigned the class "datepicker" - but I just get a normal text field when visiting the page.
Any help would be appreciated.