t-test as a randomisation test

Can I do a randomization test using a simple t-test? In particular, I have data and already checked the difference in group means of dependant variables by using t-test, but I also would like to check if control variables (e.g., age, gender, etc) in both groups are randomized to make sure the difference in values of control variables between two groups does not affect the main results? The central question is can I do that with t-tests or there are other appropriate methods that I should implement here?