HelpfulGardener.com

My Apple Tree always seems to get riddled with worms in its fruit. I was hoping someone would know of an organic deterrent that would stop these annoying creatures from ruining these delicious apples.

Brian, the first step is to identify the worms. Take or send a sample to your local county extension agent or SDSU in Brookings. If there is a commercial orchard or a large hobby orchard near by they might be able to help too.

There are very few worms(maggots) that actually get inside an apple. By far the major culprit is the Codling moth
She lays her eggs on the apples on warm days between roughly late May to late July .
Therefore the window to be able to combat her is the interval between her laying her egg and it hatching and burrowing into the apple. Once it's inside there's nothing you can do.
If you don't want to spray then the only other option is to get a pheromone trap from your garden centre for Codling Moths.
These traps capture the males that are attracted by a scent that the female gives out when she's looking for a mate. The traps carry an artificial scent that mimics this.
No other creatures are attracted ...so you get an accurate idea as to how bad the attack is.
Growers use this to guide them when to spray...low count no need...high count, wait for the female to lay and ten days later spray as the eggs hatch.
In the garden the trap can act as a disrupter, catching most of the males and leaving the females with no mates.
There are organic solutions. .....nematodes that attack the worms before they eat into the apple are available, as are Granulosis virus sprays. But that can be an expensive route for the gardener.

It is called, Fruit Tree Spray. I buy it at local hardware store. Lowes and home depot have it too.

What Lowes sells is called Bonide Fruit Tree Spray and it is DEFINITELY not organic.

Active ingredients: Captan 12%, Malathion 6%, Carbaryl .3%

OP specifically asked about organic spray.