Unfortunately there is not an official tinder profile search. However, Albion Services is the Tinder profile search tool that records Tinder users for its customers and compiles those reports into a free global database accessible here.
If you are looking for more than just a historical record search you can also find current profiles using our primary service, at here
If you find the profile you are looking for on Tinder we congratulate you and we recommend you take the time to match with them and then message the person to verify they are actively using the service. It is not unheard of for people who use Tinder to leave old accounts hanging around. One thing you can do is use the tinder web client so that you can bookmark their profile. This makes its very easy to check up on them again later to determine if they are actively using Tinder. For example if they upload a new image, change their biography text, if their location changes that is a sure sign they are still using the service.