I have always had worms in ears in corn when I picked them. The later in the season, the worse they got. Last year I read in a gardening book about adding 3 or 4 drops of mineral oil when the silk first emerged. works great! Is this an acceptable practice for organic gardening? If not, what and how.

There is no need to use any form of mineral oil or vegetable oils as a pesticide for corn pests. I have been growing sweet corn now for over 7 years in a 100% sustainable, no-till farming style, with the classic "3 sisters" companion planting technique (corn family + beans/peas family + squash/cucumber/melons family), and I have never had a worm problem, and all my corn ears are filled out!

I use a thick mulch of compost and/or legume/grain green manure to enrich the soil and supply lots of nitrogen to start off with in my long no-till beds.

Then I feed my corn weekly a strong dose of high nitrogen aerobic compost tea (sometimes 2-3 times a week during the hottest months). I use lots of horse manure and fish scraps in my compost and extra high nitrogen organic matter in my tea brews too. I use dry molasses and plain sugar in all my tea brews to get more microbial decompostion in the tea, and ultimately in the soil.

By using the aerobic tea in both a foliar/soil drench method with a bottle or cup and a 5 gallon bucket, at application time, I not only feed the heavy feeding corn, but the high microbial tea acts as a force field to repel the potential pesty worm larvae from ever getting inside my corn ears.

The close companion planting around the corn stalks also greatly repel pests.

Hope that helps, my friend.
Happy Gardening!

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The entire Kingdom of God can be totally explained as an Organic Garden (Mark 4:26)
William Cureton

To answer your question, yes, mineral oil applied is considered an organic technique. I have had better results using Bt applied when the silks start forming.