A trust can't own an individual retirement account (IRA) since a trust is not an individual. If you absolutely wanted to put the assets inside the IRA into a trust, then you'd need to report the value of the entire IRA on your income tax return for the year that you put the IRA into the trust. You should compare the increase in income taxes with your desire/need to control the IRA assets within a trust. Some people might want to shelter the IRS assets in a trust from creditors, in-laws, or state government to be eligible for Medicaid.
In the alternative, a trust can be beneficiary of an IRA.
However, the trust must either pay out the entire IRA
within 5-years of your death
(if you die before you begin withdrawing from your IRA)
or over your life expectancy on the day of your death
(if you die after you begin withdrawing from your IRA).
[The IRS estimates a 5-year life expectancy when you reach age 92 and a 27-year life expectancy when you reach age 60.]
In comparison, if an individual is the IRA beneficiary, instead of a trust, the IRS must pay out the entire IRA
within 10-years of your death
(if you die before you begin withdrawing from your IRA)
(However, if that individual is your spouse, minor child, disabled, chronically ill or someone less than 10 years younger than you, then that individual beneficiary can get pay outs over their life expectancy, when you die before you begin withdrawing from your IRA)
or over the life expectancy of the individual beneficiary
(if you die after you begin withdrawing from your IRA).
So, having your trust as the IRA beneficiary will most likely shorten the payout period for the IRA and increase the income taxes owed during payout. You would again need to compare the increase income taxes with your desire/need to control the IRA assets within a trust after your death.