I have been searching many websites for source code of AES whether it is ECB, CBC, CTR or any other method but can't find any. Can anyone please help me in getting the source code? I have to implement timing analysis on that code to see whether the code is leaky or non-leaky.
As already mentioned in the comments to your question, implementations of AES are aplenty on Github, depending on the language you want to use and on the type of requirements you have, including the original ANSI C reference implementation.
However, if you are interested in timing analysis of AES implementations, you might as well want to take a look at the Dudect code.
Dudect comes from a paper named "Dude, is my code constant time?", it is a tool meant to detect timing discrepancies using Welch's t-test. It compares actual runs of a given source code against the null hypothesis that the code running is constant time.
It notably features as an example of variable time code a T-tables implementation of AES, which is a typical example of variable-time AES implementation. But it also bundles another example, which is a bitsliced constant-time AES implementation, to show the differences between variable time and constant time code.