Hand Tremor Tracker 4+‎

Hand Tremor Tracker is the most accurate hand tremor measurement tool available on the App Store.

The application uses sensitive built-in device sensors to measure fluctuations of the device in three-dimensional axes. When the user holds their phone on top of their hand, the fluctuations of the holding hand become fluctuations of the device, allowing us to measure current hand tremor. See the references at the end of the description for more information.

How to use:
1) Place your phone on top of your hand.
2) Tap the measure button to initiate a new measurement.
3) The application takes about 10 seconds to measure your current hand tremor.

The application requires a paid subscription. A free trial is available. Subscriptions are automatically renewed and can be canceled at any time. Upon purchase of a subscription, Apple's Terms of Service and Privacy Policy apply: https://www.apple.com/legal/internet-services/itunes/dev/stdeula/

Consider seeking a doctor’s advice in addition to using this app and before making any medical decisions.

References:
1) Tamper Sensing using Low-Cost Accelerometers
Source: http://www.diva-portal.org/smash/get/diva2:538868/FULLTEXT01.pdf
Specifically see section: "3.4.5 Malign movement - Handholding"  
Methodologies used in the article (Euclidean vector calculation & Pythagorean theorem calculation) are the same methodologies used within the Hand Tremor Tracker application.
2) A smartphone-based system for detecting hand tremors in unconstrained environments
Source: https://www.researchgate.net/publication/307946579_A_smartphone-based_system_for_detecting_hand_tremors_in_unconstrained_environments
Specifically see section: "2.3 Detection of tremors with smartphones"  
Quote: "Results with the smartphone application are highly correlated with the clinical scales."