While pre-trained large language models (LLM) like BERT have achieved state-of-the-art in several NLP tasks, their performance on tasks with additional grounding e.g. with numeric and categorical features is less studied. In this paper, we study the application of pre-trained LLM for Click-through-rate (CTR) prediction for product advertisement in e-commerce, which is challenging because the model needs to a) learn from language as well as tabular data features, b) maintain low-latency (<5 ms) at inference time, and c) adapt to constantly changing advertisement distribution. We first show that scaling the pre-trained language model to 1.5 billion parameters significantly improves performance over conventional CTR baselines. We then present CTR-BERT, a novel lightweight cache-friendly factorized model for CTR prediction that consists of twin-structured BERT-like encoders for text with a mechanism for late fusion for text and tabular features. We train the CTR-BERT model using cross-architecture knowledge distillation (KD) and empirically study the interaction between KD and distribution shift in this setting, by a) experimenting with pre-training, distillation pre-finetuning and fine-tuning strategies b) factorizing features based on their distribution shift time scales, that allows the model to readily adapt and be re-trained. Finally, we show that CTR-BERT significantly outperforms a traditional CTR baseline with a 2.3\% relative ROC-AUC lift in offline experiments and a 2\% CTR lift in an online experiment.