No, you cannot apply for a visa at the airport. You need to have an e-Visa before travelling to India. Then you can get the visa stamp in your passport when you arrive.
Citizens of 160 countries, including the United States, can apply for an e-Visa. The e-Visa is for people visiting India for business, treatment, recreation, sightseeing, visiting friends or relatives and so on. People of Pakistani origin cannot get an e-Visa.
The e-Visa is emailed to you within a few days of you applying online. You need to print the e-Visa off and take it to India with you. When you arrive in India, you will get a visa stamp in your passport.