Raj and Anu were set up in a mutually agreed-upon arranged marriage by V.M. Koothrappali. They went on their first date in "The Procreation Calculation" and became engaged in the same episode.

In "The Imitation Perturbation", they attended Leonard and Penny's Halloween party, with Raj dressing up as Ruth Bader Ginsburg while Anu dressed up as the U.S. Constitution.

In "The Consummation Deviation", Raj and Anu have a set their wedding date as Valentine's Day 2019. The wedding will take place in India and Anu's family is doing most of the planning. In the same episode, Anu suggests that they have sex and Raj has a temporary relapse of his selective mutism. They end up talking throughout the night and have sex in the shower the next morning.