Random numbers are essentially required for various cryptographic applications. It is ideal to use nondeterministic random number generators in cryptography field since they are able to generate high-quality random numbers. In this paper, a Ring Oscillator (RO) based True Random Number Generator (TRNG) that can be used in cryptographic applications was developed. In this system, random numbers are generated by non-periodic sampling. Sinusoidal iterator with chaotic behavior was used for generation of non-periodic sampling signals. In TRNG system; three different scenarios, each of which contains three inverters, with 25, 10 and 5 RO circuits were implemented on FPGA environment. Randomness tests of numbers that are generated by TRNG with non-periodic sampling were carried on according to the NIST 800.22 test suit. The results have shown that the proposed system can be used in the cryptographic systems.