This paper presents angular characteristics for high-speed railway (HSR) channels, based on virtual single-input multiple-output (SIMO) measurements. A virtual array measurement scheme is investigated and used to generate SIMO channel impulse responses (CIRs) from single-antenna measurements in three typical HSR scenarios, including obstructed viaduct, deep cutting, and open station. According to the multi-antenna data, angle of arrival (AOA) is extracted using the Unitary ESPRIT (Estimation of Signal Parameters by the Rotational Invariance Techniques) algorithm, and is compared to the theoretical result. Power angular spectrum (PAS) and corresponding angular spread (AS) are provided, and the AS results in the three HSR scenarios are modeled and compared. These angular characteristics can fulfill the gap of multi-antenna channel models and provide the reference for the assessment of multi-antenna technologies in HSR scenarios.