The invention provides an acceleration control method and device of a rotary hydraulic system and an excavator. The acceleration control method includes the following steps: step10, acquiring the current pressure of a rotary pump; step20, judging the relationship between the current pressure and threshold pressure, and executing the step30 when the current pressure is larger than the threshold pressure; step30, reducing the flow control current of the rotary pump by a first preset value to acquire a flow control current of the next control cycle so as to control the flow of the rotary pump; step40, executing the step10, the step20 and the step30 in a circulating mode till the current pressure is small than or equal to the threshold pressure. Because a gradual changing mode is adopted to control the flow of the rotary pump, the stability and safety of rotary motion of engineering equipment can be guaranteed, the service life of the engineering equipment can be prolonged, and meanwhile the situation that the pressure output by the rotary pump is larger than the threshold pressure when the target value of an operating handle is too large and the flow control current directly increases to the target value is avoided.