Your question in a bit unclear in that you don't specify whether you are talking about true random numbers or pseudo-random numbers, so I will answer both.
True Random Numbers
You are correct that functional programs can't produce true random numbers. But neither can imperative programs. Computers are still deterministic machines, regardless of whether they are running a C program or a Haskell program.
Pseudo-Random Numbers are generated by a Pseudo-Random Number Generator (aka PRNG). PRNGs are just algorithms like any other algorithm. They can be expressed in a functional language just as well as they can be expressed in an imperative language.
So, there is really no difference between functional languages and imperative languages when it comes to random numbers. Both can compute pseudo-random numbers and neither can compute true random numbers (since they can't be computed at all).
in functional programming "true" randomness cannot be achieved since in FP functions are pure/idempotent and return the same value irrespective of number of invocations without any side effects.
Again, the same thing is true for imperative programming. If you call
srand with the same seed number, you will deterministically get the same pseudo-random number sequence from
rand, every time.
The only way to get true randomness is through I/O. But, functional languages can model I/O just fine, whether that be with an I/O Monad (or something more specialized like a
Random monad), linear types, world types, effect types, an effect system, or like Scala, ML, Clojure, and F♯ do it, by simply allowing them and trusting the programmer to not make mistakes.
So, in other words, it makes no sense to be asking about Random Numbers specifically. A PRNG is just a function, so if you are asking how functional programming can be used to deal with pseudo-random numbers, then you should rather ask how functional programming can be used to deal with functions, because there is nothing special about a PRNG, it's just a function. And True Randomness is just I/O, so again, it doesn't make sense to ask about them specifically.
If you accept that you can write functions in FP, then you must also accept that you can write PRNGs in FP. And if you accept that you can read the clock, read input from the user, read a file, access a database, access the web, etc., then you must also accept that you can read True Random Numbers. (In fact, on Unix, for example, device drivers are typically exposed as files, and a true random number device would typically be exposed as a file you read from. And there is a web service that serves true random numbers.)