Fiber nonlinearity is one of the major impairments for long-haul transmission systems. Therefore, estimating the nonlinear signal-to-noise ratio (SNR) is indispensable to guarantee the quality of transmission and manage the operation of optical networks. The deep neural network (DNN) has been successfully applied for the SNR estimation. However, the performance substantially degrades, when the mega dataset is inaccessible. Here, we demonstrate an accurate SNR estimation based on the data augmentation (DA)-assisted DNN with a small-scale dataset in the frequency domain. When the 95-GBaud dual-polarization 16 quadrature amplitude modulation (DP-16QAM) signal with variable optical launch powers from -2 to 4-dBm is numerically transmitted from 80-km to 1520-km standard single-mode fiber (SSMF), we identify that, in comparison with traditional DNN scheme, the DA allows the reduction of the training dataset size by about 60% while keeping the same mean absolute error (MAE) as 0.2-dB of SNR estimation. Meanwhile, the DA-assisted DNN scheme can reduce the MAE by about 0.14-dB compared with the traditional DNN scheme, when both SNR estimation schemes use 100 raw datasets which contain 700 symbols. Due to these observations, the DA-assisted DNN scheme is promising for field-trial nonlinear SNR estimation, especially when the collection of mega datasets is inconvenient.