Rock geochemistry can accurately and effectively delineate geological anomalies, providing clear instructions for geological prospecting and playing a crucial role in mineral resource exploration. However, traditional geochemical exploration methods are based on ground sampling and laboratory chemical analysis, which are time-consuming, laborious, and inefficient. This study collected 191 rock samples, and the Cu content and spectral data were obtained using chemical analysis and an analytical spectral device (fieldspec3, portable spectrometer) in the laboratory. However, spectral preprocessing and estimation models are critical for estimation accuracy. Therefore, this study discusses the potential of fractional derivative spectroscopy and a model method for estimating rock Cu content. The results show the following. (1) Compared with the original spectrum and the integer-order derivative spectrum (first and second derivative), the fractional-order derivatives (FODs) can better highlight the spectral details. With the increased order of derivatives, the characteristic band becomes more obvious. (2) The combined FOD and random forest (RF) model performs best for the full sample data. The coefficient of determination (R2) is as high as 0.766, the mean absolute error (MAE), and the ratio of the performance to deviation (RPD) are 9.09 and 2.067, respectively, significantly better than partial least squares (PLS) models (R2 = 0.598, MAE = 13.389, RPD = 1.577) and the K-nearest neighbor (KNN) algorithm (R2 = 0.686, MAE = 10.905, RPD = 1.786). (3) For the samples with Cu content less than 45 mg/kg, using the PLS method and samples with Cu content greater than 45 mg/kg and the RF method to build the estimation model achieved better overall results (R2 = 0.881, MAE = 6.697, RPD = 2.899). Therefore, combining FOD technology and the segmental modeling method can effectively and quickly estimate the Cu content in rocks, providing technical support for estimating Cu content in rocks from aerial imaging hyperspectral images.