BACKGROUND: The clinical benefits of intensity-modulated proton therapy (IMPT) compared with intensity-modulated radiation therapy (IMRT) for patients with oropharyngeal squamous cell carcinoma remain uncertain with respect to treatment-related effects on physical function and quality of life. We aimed to compare late functional, patient-reported, disease control, and survival outcomes between IMPT and IMRT. METHODS: We did a phase 3 trial (TORPEdO) in 20 UK National Health Service hospitals. We randomly assigned (2:1) patients with locally advanced oropharyngeal squamous cell carcinoma to IMPT or IMRT (70 Gy in 33 fractions, for 6·5 weeks) with two cycles of high-dose cisplatin (100 mg/m2, every 3 weeks). Co-primary endpoints at 12 months were gastrostomy-tube dependence (use of feeding tube for nutrition) or severe weight loss (≥20% from baseline) and University of Washington quality of life (UW-QoL) mean physical composite score for saliva, taste, chewing, swallowing, speech and appearance. The study was registered with the ISRCTN registry, ISRCTN16424014; recruitment is complete and follow-up is ongoing. FINDINGS: Between Feb 25, 2020, and June 13, 2023, we randomly assigned 205 patients (99 [48%] with T3 or T4 disease and 44 [22%] with bilateral neck lymph node involvement (N2[c]); 136 [66%] to IMPT and 69 [34%] to IMRT). 163 (80%) patients were male and 42 (20%) were female. Ethnicity data were self-reported by 177 (86%) patients; most were White British (167 [94%]). At 12 months, gastrostomy-tube dependence occurred in two (2%) of 119 patients in the IMPT group and in one (2%) of 59 patients in the IMRT group and severe weight loss occurred in 20 (18% [97·5% CI 11 to 28]) of 110 patients in the IMPT group and in three (6% [1 to 17]) of 53 patients in the IMRT group (combined odds ratio 2·80 [97·5% CI 0·75 to 10·4]; p=0·079). Mean UW-QoL physical composite scores at 12 months were 78·3 in the IMPT group versus 77·1 in the IMRT group (difference 1·3 [97·5% CI -3·7 to 6·2]; p=0·56). There were 14 serious adverse events in 12 patients (nine assessed as unrelated to the study treatment [four in the IMPT group and five in the IMRT group] and five study treatment-related [one IMPT vs four IMRT]); the most common events were acute kidney injury (five [36%]) and thromboembolism (four [29%]). There were no treatment-related deaths. At a median follow-up of 28·3 months (IQR 26·5 to 39·3), 24-month freedom from loco-regional recurrence rates were 94% (99% CI 86-98) in the IMPT group versus 97% (82-100) in the IMRT group (hazard ratio [HR] 2·6 [99% CI 0·3 to 20·3; 95% CI 0·5-12·4]; p=0·24), and overall survival rates were 95% (86 to 98) in the IMPT group versus 95% (81-99) in the IMRT group (HR 1·6 [99% CI 0·3 to 8·8; 95% CI 0·4 to 5·9; p=0·47). INTERPRETATION: IMPT and IMRT had similar late physical quality of life scores, gastrostomy-tube dependence, local control, and overall survival. In health-care settings where IMPT is not used routinely for oropharyngeal squamous cell carcinoma, IMRT remains the standard of care. FUNDING: Cancer Research UK.