Traditionally, tenure committees have relied on bibliometric indicators, such as the h-index and journal impact factors, to measure research output of individuals and to determine hiring and promotion decisions. But quantitative metrics are only one possible way to measure impact, and they have well-documented limitations. Altmetrics, and other forms of metrics, can help researchers gauge their impact in ways that can't be determined by traditional metrics.
From Konkiel, S., Sugimoto, C., Williams, S. (2016) "The Use of Altmetrics in Promotion and Tenure"
Including the raw numbers or Altmetric score is not enough; you will need to put the numbers in context. The key is to make the numbers meaningful.
It's not enough to provide raw numbers or counts; explain why they are important and provide context for your data. Always provide the source of your information, too.
The following are examples of how you might incorporate metrics into your CV:
Real life example of a C.V. incorporating Altmetrics, from Trevor A. Branch, School of Aquatic and Fishery Sciences at the University of Washington.
Guide to Preparing a Dossier for Promotion or Tenure (University of Colorado Denver Medical School) : An extensive guide that contains information on how to showcase and explain metrics on a tenure dossier. Includes examples of showcasing impact in a clinical setting.