Comparing proportions

I have a sample of 65 participants. 20 chose A. 18 chose B. 14 chose C and 13 chose D. What is the suitable test to determine if there is significant difference in the proportions?

It's not completely clear that I have understood correctly, but I think you're asking whether the proportions choosing A, B, C and D are consistent with the population proportions being $(\frac{1}{4},\frac{1}{4},\frac{1}{4},\frac{1}{4})$.

If that's the case, this is just a chi-squared goodness of fit test.

(Searching on chi-squared goodness of fit test or chi-square goodness of fit test will turn up many hits here, a few of which will relate to your kind of problem.)

Since this looks like the particular numbers may be from a self-study question, I won't do the problem itself, but I will explain the calculation of the test statistic.

Given the 65 participants you compute the expected count in each cell, $E_i = 65/4,\, i=1,2,3,4$. The observed counts, $O_i$ are given in your question.

You then compute the chi-square statistic, $X^2 = \sum_{i=1}^4 \frac{(O_i-E_i)^2}{E_i}$, which under the null hypothesis has a $\chi^2$ distribution with three degrees of freedom.

Most stats packages can do this work for you, but it's a few moments to do by hand if you have chi-square tables.