<p>The objective of this paper is to develop a novel approach to univariate constrained recurrent rational fractal interpolation using a recurrent iterated function system. This method constructs rational functions with cubic polynomials in the numerator and linear polynomials in the denominator, enhancing flexibility and computational efficiency compared to traditional cubic interpolation techniques. We rigorously establish the uniform error bound of the Recurrent Rational Fractal Interpolation Function with the original data generating function and impose necessary constraints to maintain the univariate recurrent rational structure that lies (i) between two piecewise linear functions, (ii) between two straight lines, and (iii) within a bounded rectangular region, and monotonicity-preserving of univariate recurrent rational fractal interpolation. We present several numerical examples to illustrate the functionality and potential applications of recurrent rational fractal interpolation functions.</p>