Code generation refers to the automatic generation of source code based on a given programming specification, which has garnered significant attention particularly with the advancement of large language models (LLMs). However, due to the inherent complexity of real-world problems, the LLM-generated code often fails to fully align with the provided specification. While state-of-the-art agent-based techniques have been proposed to enhance LLM code generation, they overlook the critical issue of specification perception, resulting in persistent misalignment issues. Given that accurate perception of programming specifications serves as the foundation of the LLM-based code generation paradigm, ensuring specification alignment is particularly crucial. In this work, we draw on software requirements engineering to propose Specine, a novel specification alignment technique for LLM code generation. Its key idea is to identify misaligned input specifications, lift LLM-perceived specifications, and align them to enhance the code generation performance of LLMs. Our comprehensive experiments on four state-of-the-art LLMs across five challenging competitive benchmarks by comparing with ten state-of-the-art baselines, demonstrate the effectiveness of Specine. For example, Specine outperforms the most effective baseline, achieving an average improvement of 29.60% across all subjects in terms of Pass@1.