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Blockchain as a Service (BaaS) combines features of cloud computing and blockchain, making blockchain applications more convenient and promising. Although current BaaS platforms have been widely adopted by both industry and academia, concerns arise regarding their performance, especially in job allocation. Existing BaaS job allocation strategies are simple and do not guarantee load balancing due to the dynamic nature and complexity of BaaS job execution. In this paper, we propose a deep reinforcement learning-based algorithm, Balanced-DRL, to learn an optimized allocation strategy in BaaS based on analyzing the execution process of BaaS jobs and a set of job scale characteristics. Following extensive experiments with generated job request workloads, the results show that Balanced-DRL significantly improves BaaS performance, achieving a 5% to 8% increase in job throughput and a 5% to 20% decrease in job latency.