If I deposit money as cash does it count as direct deposit ? I am asking before I got an offer from a bank if I do one direct deposit within 90 days. Free money is good.
Well, it's directly depositing money in your account, but Direct Deposit is something completely different: https://en.wikipedia.org/wiki/Direct_deposit
Direct deposits are most commonly made by businesses in the payment of salaries and wages and for the payment of suppliers' accounts, but the facility can be used for payments for any purpose, such as payment of bills, taxes, and other government charges. Direct deposits are most commonly made by means of electronic funds transfers effected using online, mobile, and telephone banking systems but can also be effected by the physical deposit of money into the payee's bank account.
Thus, since the purpose of DD is to eliminate checks, I'd say, "no", depositing cash directly into your account does not count as the requirement for one Direct Deposit within 90 days.
As RonJohn points out, direct deposit is something very different. What's going on here is that they are trying to exclude the "customers" that open the account simply for the premium and then close it again as soon as the terms of the offer have been met. Most people have only one regular source of direct deposit money, either their paycheck or a retirement check. This acts to make it hard for them to simply take the offer and run.