It depends on how your hardware is configured. Normally, reading is not CPU-intensive, thanks to DMA. It may be very expensive though, if it initiates swap-out of other applications. But there is more to it.
Don't read a huge file at once if you can
If your file is really big, you should use mmap or sequential processing, when you don't need to read a whole file at once. Try to consume it by chunks is possible.
For example, to sum all values in a huge file, you don't need to load this file into the memory. You can process it by small chunks, accumulating the sum. Memory is an expensive resource in most situations.
Reading is sequential
Does the file reading operation need to consume 1 core?
Yes, I think most low-level read operations are implemented sequentially (consume 1 core).
You can avoid blocking on read operation if you use asynchronous I/O, but it is just a variation of the same "read by small chunks" technique. You can launch several small asynchronous read operations at once, but you have always to check if an operation has finished before you use the result.
See also this Stack Overflow answer to a related question).
Reading and computing in parallel
Previously I just create 2 threads, one to read file and one to compute? Should I create an additional thread to do compute?
It depends, if you need all data to start computations, than there is no reason to start computation in parallel. It will have to wait effectively until reading is done.
If you can start computing even with partial data, likely you don't need to read the whole file at once. And it is usually much better not to do so with huge files.
What is your bottleneck — computation or IO?
Finally, you should know if your task is computation-bound or input-output bound. If it is limited by the performance of input-output subsystem, there is little benefit in parallelizing computation. If computation is very CPU-intensive, and reading time is negligible, you can benefit from parallelizing computation. Input-output is usually a bottleneck unless you are doing some number-crunching.