We consider a symbol-asynchronous uplink non-orthogonal multiple access (NOMA) model with equal-power transmission, where K users transmit their codewords to a common receiver in an asynchronous manner. The received signal vector is an asynchronous superposition of all users' codewords. Due to the equal-power transmission, such signal detection scheme as successive interference cancellation (SIC) is invalid. We propose a message passing (MP) detection for the symbol-asynchronous NOMA system and analyze its performance by deriving a signal-to-interference-plus-noise ratio (SINR) of the detector output. Our analysis and simulations show that symbol asynchronization, i.e., each user has a different transmission time offset, in fact benefits signal detection, and its performance depends on the employed modulation waveform.