Automating analog circuit design remains a longstanding challenge in Electronic Design Automation (EDA). While Transformer-based Large Language Models (LLMs) have revolutionized software code generation, their application to analog hardware design is hindered by two critical limitations: (i) the scarcity of analog design datasets containing natural language description of a design and its corresponding netlist, and (ii) the inefficiency of general-purpose tokenizers (e.g., Byte Pair Encoding (BPE)) in capturing the inherent graph structure of circuits. To bridge this gap, first, we curate the largest annotated dataset of analog circuit netlists to date, comprising 31,341 netlist-natural language description pairs across all major circuit classes. Furthermore, we propose Circuit Tokenizer (CKT), a novel circuit graph tokenizer designed to encode netlist connectivity by explicitly mining frequent subcircuits. In terms of scalability, CKT overcomes the bottleneck of prior circuit graph serialization methods where vocabulary size scales linearly with maximum number of components in the dataset, n_max, (O(n_max)); instead, CKT decouples vocabulary growth from circuit complexity, achieving a constant O(1) complexity. Empirically, CKT outperforms standard BPE on circuit topology representation, reducing sequence length by 57% and achieving a 2.3x superior compression ratio using a compact, fixed vocabulary of size 512. Leveraging this optimized tokenization, we train a circuit-specific language model, CircuitFormer, a 511M parameter encoder-decoder transformer. Our model achieves 100% syntactic correctness and an 83% functional success rate across all major analog circuit categories, outperforming state-of-the-art open-source LLMs by 10% and 14%, respectively, while requiring 240x fewer parameters. The dataset is publicly available at https://huggingface.co/datasets/touhid314/cktformer-dataset.