The spaceborne Global Navigation Satellite System-Reflectometry (GNSS-R) delay-Doppler map (DDM) data collected over ocean carry typical feature information about the ocean surface, which may be covered by open water, mixed water/ice, complete ice, etc. A new method based on Doppler spread analysis is proposed to remotely sense sea ice using the spaceborne GNSS-R data collected over the Northern and Southern Hemispheres. In order to extract useful information from DDM, three delay waveforms are defined and utilized. The delay waveform without Doppler shift is defined as central delay waveform (CDW), while the integration of delay waveforms of 20 different Doppler shift values is defined as integrated delay waveform (IDW). The differential waveform between normalized CDW (NCDW) and normalized IDW (NIDW) is defined as differential delay waveform (DDW), which is a new observable used to describe the difference between NCDW and NIDW, which have different Doppler spread characteristics. The difference is mainly caused by the roughness of reflected surface. First, a new data quality control method is proposed based on the standard deviation and root-mean-square error (RMSE) of the first 48 bins of DDW. Then, several different observables derived from NCDW, NIDW, and DDW are applied to distinguish sea ice from water based on their probability density function. Through validating against sea ice edge data from the Ocean and Sea Ice Satellite Application Facility, the trailing edge waveform summation of DDW achieves the best results, and its probabilities of successful detection are 98.22% and 96.65%, respectively, in the Northern and Southern Hemispheres.