With the widespread diffusion of smartphones, Spatial Crowdsourcing (SC), which aims to assign spatial tasks to mobile workers, has drawn increasing attention in both academia and industry. One of the major issues is how to best assign tasks to workers. Given a worker and a task, the worker will choose to accept the task based on her affinity towards the task, and the worker can propagate the information of the task to attract more workers to perform it. These factors can be measured as worker-task influence. Since workers' affinities towards tasks are different and task issuers may ask workers who performed tasks to propagate the information of tasks to attract more workers to perform them, it is important to analyze worker-task influence when making assignments. We propose and solve a novel influence-aware task assignment problem in SC, where tasks are assigned to workers in a manner that achieves high worker-task influence. In particular, we aim to maximize the number of assigned tasks and worker-task influence. To solve the problem, we first determine workers' affinities towards tasks by identifying workers' historical task-performing patterns. Next, a Historical Acceptance approach is developed to measure workers' willingness of performing a task, i.e., the probability of workers visiting the location of the task when they are informed. Next, we propose a Random reverse reachable-based Propagation Optimization algorithm that exploits reverse reachable sets to calculate the probability of workers being informed about tasks in a social network. Based on worker-task influence derived from the above three factors, we propose three influence-aware task assignment algorithms that aim to maximize the number of assigned tasks and worker-task influence. Extensive experiments on two real-world datasets offer detailed insight into the effectiveness of our solutions.