The answer is, surprisingly, yes, you can have taxes in your IRA.
Normally, IRAs invest in stocks, bonds, mutual funds, and ETFs and receive interest, dividends and gains from these.
Congress felt that non-taxable entities shouldn't unfairly compete with taxable firms. Therefore, they are taxed on income from "Business Income" (in tax parlance UBTI). UBTI is taxed at trust rates. The top rate is 39.6% and kicks in quickly.
Taxes are triggered by non traditional assets like hedge funds, private-equity funds, limited partnerships, operating businesses and real estate.
So, before you invest in an non-traditional asset in your IRA, ask if it will be taxable.