I have used the new EA App to successfully purchase SimPoints for the Sims 3 game, I have done it several times in the past month or so.  It is almost "too easy" to do so. 

Here's what see with the EA App, showing Sims 3 add-ins:

Click the Sims 3 Currency and the EA App will go through the process of adding a credit card for payment.  If you have already done that you simply select the amount of SimPoints you want to buy, the EA App defaults for me to US$20.00 (2,040 SimPoints) and shows a purchase dialog.  Click the purchase button and in a few seconds you should have your newly purchased SimPoints.