Digital advertising is used to leverage Internet technologies to deliver advertisements to consumers. For an advertisement to reach a large number of audience, business owners usually relay on social media influencers to deliver advertisements messages. However, there are a large number of influencers and it is critical step for business owners to select influencers to be hired. One important measure that has been used to assist the process of selecting an influencer is the influencer engagement rate. Engagement rate measure aims to evaluate how well an influencer can attract potential customers. The current engagement rate measures depend on a simple information such as number of followers, posts, or comments on an influencer account. In this paper we propose a more sophisticated engagement rate measure based on a carful analysis of potential customers reaction to an influencer advertisements posts. The new measure works only on advertisements posts. Also, it take into account the polarity of the comments on these posts, not only their count. To efficiently compute the new engagement rate measure over large size of data, we propose machine learning (ML) approaches to generate necessarily information to compute the new engagement rate measure. We use ML approaches, in particular classifications, in two stages. First, we use classification to efficiently classify a post to an advertisement and none advertisement post. Next, we use ML based sentiments analysis approach to determine the polarity of the comments on an advertisement post. The new measure could be used to measure users engagement to any post and in a wide range of social media platforms. We tested the new engagement rate measure using Instagram influencer accounts, in specific Instafamous accounts. Compared to the current measures, our results show that this new ML based engagement rate measure suggests significantly different ranked list of potential influencers. This ranked list of influencers are more aligned with the business needs and the accepted practices in measuring successful advertisers.