The results of (115)In nuclear quadrupole resonance (NQR) measurements on PuIn3 are reported. Three of the four NQR lines of (115)In expected for nuclear spin I = 9/2 are observed. The equal spacing of these lines at 20 K yields the NQR frequency of νQ = 10.45 MHz, and the asymmetry parameter of the electric field gradient η = 0. The NQR line profile and the nuclear spin-lattice relaxation rate 1/T1 display an abrupt change at 14 K, which is associated with the onset of long-range antiferromagnetic order. The temperature dependences of the staggered magnetization MQ(T), extracted from the NQR spectra, and 1/T1 below TN = 14 K are well explained by the self-consistent renormalization (SCR) theory for spin fluctuations. In addition, the scaling between T1T and MQ(T)/MQ(0) is also consistent with the predictions of SCR theory, providing further evidence that PuIn3 is a weak itinerant antiferromagnet in which spin fluctuations around the antiferromagnetic wavevector play a major role in the system's behavior at finite temperatures.