The Brazilian software developer behind the program, uTouchLabs, describes it as a "fun way to randomly choose between two options."
"Cinema or theatre? Pizza or sushi? Skirt of dress? Marcia or Andrea? Ask the Octopus?" it says.
The user types in the options and a cartoon octopus chooses between them.
The program costs 99 US cents ($A1.12) to download from Apple's iTunes.
Paul, an octopus at an aquarium in Oberhausen, Germany, earned worldwide attention during the World Cup with his predictions, which included Spain's victory in the final against the Netherlands.
Meanwhile, Apple shares have slid due to problems with its new iPhone.
Consumers have panned the device due to reception problems.
There are rumours Apple will recall the new iPhone, another factor leading to the company's share dip.
