I purchased a rental property with equity from my primary residence.

Yes, if the new property is currently available as a rental, you can deduct this interest as a rental expense. If you just took out a separate mortgage on your home, then it's easy, just report all the interest as a rental expense.  This can get a little complicated if it is a refinance and you have debt that pertains to both your primary home and your rental.

You can divide this mortgage up between the portion that is considered home acquisition debt and the portion that is home equity debt that you used to purchase your rental property. To do it in TurboTax, start with your personal deduction for the home acquisition debt:

1. Enter your Form 1098 as a personal deduction in Federal > Deductions & Credits > Your Home > Mortgage Interest & Refinancing
2. Enter only the portion of the interest that was home acquisition debt. If your refinance was for $700,000 and you used $200,000 on the rental, enter 5/7 of the interest. The next year if your outstanding mortgage principal is $680,000, your rental interest would still be the interest on $200,000 but your personal interest deduction would be for the interest on $480,000. 
3. Select the box that says The interest amount I entered is different than what's on my 1098. You will attach an explanation statement that states the remainder of the interest was allocated to your rental property.
4. Report the outstanding mortgage principal only as the portion that pertains to the home acquisition debt.
5. After a few screens, answer No to Is this the original loan used to buy the property? in Let's get some details about this loan
6. Answer Yes to Is this loan a HELOC or refinance?
7. Answer No to Did you take cash out? You are only reporting the home acquisition debt here.

You will report the rental interest as a rental expense.

1. Select Start/Revisit next to Federal > Wages & Income > Rentals, Royalties, and Farm > Rental Properties and Royalties (Sch E)
2. Report it as Other Interest.