In intensity-modulated proton therapy (IMPT), protons are used to deliver highly conformal dose distributions, targeting tumors, and sparing organs-at-risk. However, due to uncertainties in both patient setup and relative stopping power (RSP) calculation, margins are added to the treatment volume during treatment planning, leading to higher doses to normal tissues. Cone-beam computed tomography (CBCT) images are taken daily before treatment; however, the poor image quality of CBCT limits the use of these images for online dose calculation. In this work, we use a deep-learning-based method to predict RSP maps from daily CBCT images, allowing for online dose calculation in a step toward adaptive radiation therapy. Twenty-three head-and-neck cancer patients were simulated using a Siemens TwinBeam dual-energy CT (DECT) scanner. Mixed-energy scans (equivalent to a 120kVp single-energy CT scan) were converted to RSP maps for treatment planning. Cone-beam computed tomography images were taken on the first day of treatment, and the planning RSP maps were registered to these images. A deep learning network based on a cycle-GAN architecture, relying on a compound loss function designed for structural and contrast preservation, was then trained to create an RSP map from a CBCT image. Leave-one-out and holdout cross validations were used for evaluation, and mean absolute error (MAE), mean error (ME), peak signal-to-noise ratio (PSNR), and structural similarity (SSIM) were used to quantify the differences between the CT-based and CBCT-based RSP maps. The proposed method was compared to a deformable image registration-based method which was taken as the ground truth and two other deep learning methods. For one patient who underwent resimulation, the new planning RSP maps and CBCT images were used for further evaluation and validation. The CBCT-based RSP generation method was evaluated on 23 head-and-neck cancer patients. From leave-one-out testing, the MAE between CT-based and CBCT-based RSP was 0.06±0.01 and the ME was -0.01±0.01. The proposed method statistically outperformed the comparison DL methods in terms of MAE and ME when compared to the planning CT. In terms of dose comparison, the mean gamma passing rate at 3%/3mm was 94% when three-dimensional (3D) gamma index was calculated per plan and 96% when gamma index was calculated per field. The proposed method provides sufficiently accurate RSP map generation from CBCT images, allowing for evaluation of daily dose based on CBCT and possibly allowing for CBCT-guided adaptive treatment planning for IMPT.