In this paper, we propose a model to perform style transfer of speech to singing voice. Contrary to the previous signal processing-based methods, which require high-quality singing templates or phoneme synchronization, we explore a data-driven approach for the problem of converting natural speech to singing voice. We develop a novel neural network architecture, called SymNet, which models the alignment of the input speech with the target melody while preserving the speaker identity and naturalness. The proposed SymNet model is comprised of symmetrical stack of three types of layers - convolutional, transformer, and self-attention layers. The paper also explores novel data augmentation and generative loss annealing methods to facilitate the model training. Experiments are performed on the NUS and NHSS datasets which consist of parallel data of speech and singing voice. In these experiments, we show that the proposed SymNet model improves the objective reconstruction quality significantly over the previously published methods and baseline architectures. Further, a subjective listening test confirms the improved quality of the audio obtained using the proposed approach (absolute improvement of 0.37 in mean opinion score measure over the baseline system).