By solving the (3+1)-dimensional free-space Schrödinger equation in circular cylindrical coordinates, we have systematically analyzed the propagation of chirped Airy-circular (CAiCi) wave packets. The complex amplitude of the CAiCi wave packets is constructed by the Airy function, the Gaussian function, and the confluent hypergeometric function. We find that the CAiCi wave packets are some coaxial ring pulses stacked along the temporal domain in the initial position, which are modulated by the chirped factor, the initial velocity, the distribution factor, and the propagation distance. Meanwhile, the wave packets will appear to undergo intensity attenuation, diffusion, convergence, and so on. We can also modulate the shape of the wave packets and change their optical properties by altering the mode numbers. Furthermore, we analyze the evolution properties of the wave packets in detail from the aspects of the gradient force, the scattering force, phase, the Poynting vector, and the angular momentum, and find some interesting phenomena.