Metal-organic frameworks (MOFs) are materials with a high degree of porosity that can be used for many applications. However, the chemical space of MOFs is enormous due to the large variety of possible combinations of building blocks and topology. Discovering the optimal MOFs for specific applications requires an efficient and accurate search over countless potential candidates. Previous high-throughput screening methods using computational simulations like DFT can be time-consuming. Such methods also require the 3D atomic structures of MOFs, which adds one extra step when evaluating hypothetical MOFs. In this work, we propose a structure-agnostic deep learning method based on the Transformer model, named as MOFormer, for property predictions of MOFs. MOFormer takes a text string representation of MOF (MOFid) as input, thus circumventing the need of obtaining the 3D structure of a hypothetical MOF and accelerating the screening process. By comparing to other descriptors such as Stoichiometric-120 and revised autocorrelations, we demonstrate that MOFormer can achieve state-of-the-art structure-agnostic prediction accuracy on all benchmarks. Furthermore, we introduce a self-supervised learning framework that pretrains the MOFormer via maximizing the cross-correlation between its structure-agnostic representations and structure-based representations of the crystal graph convolutional neural network (CGCNN) on >400k publicly available MOF data. Benchmarks show that pretraining improves the prediction accuracy of both models on various downstream prediction tasks. Furthermore, we revealed that MOFormer can be more data-efficient on quantum-chemical property prediction than structure-based CGCNN when training data is limited. Overall, MOFormer provides a novel perspective on efficient MOF property prediction using deep learning.