Absolutely! It's a great idea to ask guests to review your property. It shows that you care about their feedback and improving your business.
You can use the resources in the Management Center to remind guests to write reviews. Log in and click the “Reviews” tab in the menu, then select "Review Express" to email recent visitors to write a review on TripAdvisor. More on Review Express can be found here. You must be a registered owner to access your property's Management Center page. To register, go to tripadvisor.com/Owners and follow the instructions.
Just keep in mind that you can't offer guests any incentives for writing reviews. We also recommend that guests submit their reviews when they return home, from their own PC or mobile devices.