All a pension is is an investment account that provides a defined benefit after retirement. So sure, you can set up a pension for yourself; just invest in some account (it can even be an IRA) and after you retire just set up a specific distribution (letting the rest of the account continue to grow). Or use the money to purchase some sort of annuity if you want to formalize the payment.
The point is that pensions are not magical - the money you get must come from somewhere. For company pensions, the company funds the pension and must ensure that it has invested enough to be able to make the payments it promises. If you set up your own pension, you must fund it.