Transfer learning on tabular data is challenging due to disparate feature spaces across domains, in contrast to the homogeneous structures of image and text. Large language models (LLMs) offer a knowledge base to improve the limited effectiveness of cross-domain transfer learning for tabular data. However, LLM performance often stagnates due to subjective text prompts and the computational limitations of in-context learning. We present a novel language-to-tabular context-learning method that uses attention-specific transformer weights, enabling seamless transfer learning across disparate tabular data sets. The LLM attention transplant mechanism facilitates a domain-agnostic transfer learning, eliminating the need for shared features between tables, LLM prompt engineering, and large-scale pretrained models. Our experiments using ten pairs of disjoint source-target data sets and 12 baseline methods demonstrate the superiority of the proposed LLM-attention transplant for transfer learning (LATTLE) method over traditional ML models, state-of-the-art deep tabular architectures, and models trained on thousands to billions of tabular samples. The proposed cross-domain attention transfer demonstrates an effective solution for adapting LLMs to learning non-text tabular data in a low-resource environment. The source code of the LATTLE implementation is publicly available.