The growing number of data centers consumes a vast amount of energy for processing. There is a desire to reduce the environmental footprint of the IT industry, and one way to achieve this is to use renewable energy sources. A challenge with using renewable resources is that the energy output is irregular as a consequence of the intermittent nature of this form of energy. In this paper, we propose a simple and yet efficient latency-aware workload scheduler that creates an energy-agile workload, by deferring tasks with low latency sensitivity to periods with excess renewable energy. The scheduler also increases the overall efficiency of the data center, by packing the workload into as few servers as possible, using neural-network-based predictions of resource usage on an individual task basis to avoid unnecessarily provisioning an excess number of servers. The scheduler was tested on a subset of real-world workload traces, and real-world wind-power generation data, simulating a small-scale data center co-located with a wind turbine. Extensive experimental results show that the devised scheduler reduced the number of servers doing work in periods of low wind-power production up to 93% of the time, by postponing tasks with a low latency sensitivity to a later interval.