We introduce semantic form mid-tuning, an approach for transferring semantic knowledge from semantic meaning representations into transformer-based language encoders. In mid-tuning, we learn to align the text of general sentencesnot tied to any particular inference task-and structured semantic representations of those sentences. Our approach does not require gold annotated semantic representations. Instead, it makes use of automatically generated semantic representations, such as from off-the-shelf PropBank and FrameNet semantic parsers. We show that this alignment can be learned implicitly via classification or directly via triplet loss. Our method yields language encoders that demonstrate improved predictive performance across inference, reading comprehension, textual similarity, and other semantic tasks drawn from the GLUE, SuperGLUE, and SentEval benchmarks. We evaluate our approach on three popular baseline models, where our experimental results and analysis concludes that current pre-trained language models can further benefit from structured semantic frames with the proposed mid-tuning method, as they inject additional task-agnostic knowledge to the encoder, improving the generated embeddings as well as the linguistic properties of the given model, as evident from improvements on a popular sentence embedding toolkit and a variety of probing tasks.