By "UTP", I'm assuming you're referring to Unshielded Twisted Pair. The shielding and twisting aren't really relevant, because they're just physical characteristics of the cable itself. They don't have any bearing on the sender or receiver.
The salient point about UTP is that it uses differential transmission. That is, the data is sent down two wires at the same time, but one is inverted. The receiver uses the difference between the two signals to reconstruct the original data, eliminating any interference which may have been introduced en route.
Assuming the voltage level is safe (0-5v for most boards), you could connect each wire directly to an analog pin on the Arduino. If you read both continuously, and apply suitable thresholds/triggers in software to identify level changes, you could probably reconstruct the original signal.
It's definitely not ideal though, as ADCs are comparatively slow, and you would never be able to read both at exactly the same time. That means the transmission would have to be quite slow in order to work. The exact speed would depend on how quickly your program could poll the ADCs and process the result.
It would be much better to use some external circuitry to handle the differential signal. It could then produce a nice clean digital output which you could feed directly to any input on the Arduino. It should be able to run a lot faster, and leave your program free to do other things. Any good electronics vendor will stock a variety of ICs which would do the job, depending on your exact requirements.
Setting up your computer/laptop as a sender is a totally separate issue though. Many different ports use differential signals in some form, including ethernet, USB, and RS-232 (old DE-9 serial ports). Unfortunately, it would be very difficult to get direct control of their signal lines. You would almost certainly have to write your own device drivers, which is a pretty huge undertaking.
If you want to send serial data from your computer to an Arduino, the easiest way is just USB-to-TTL conversion. Most Arduino boards have this built-in, connected directly to the hardware serial lines on the microcontroller (which is how you upload programs/sketches). Alternatively, you can get external cables which do the conversion, and you can connect it manually to other pins, processing it using software serial.