Here are three options I can think of:
clock_gettime(CLOCK_MONOTONIC) gets the current system uptime. This is relatively unreliable because if the user reboots, this is reset. You could save the last value used and at launch use the last saved value as an offset, but the problem with this is that the time that the device was shut off for won't be calculated.
mach_absolute_time() counts the number of CPU ticks since the last reboot. It can be fetched easily through CACurrentMediaTime. Note that this can be reset simply by rebooting the device, so if changing the time is very important, I'm not so sure if you would go this way.
Network Time Protocol (NTP) is a networking protocol for synchronizing the clocks of computer systems. In practice, all NTP is is querying a time server. An iOS library for NTP can be found here.
So the first two methods do not require connectivity, while the third does. However, the third method is the only foolproof one.