Yes, it most certainly can.
Both weight loss, and what you're actually eating (your diet) can have a direct impact on your menstrual cycle.
Expect early periods when you diet
The way to think of it is that your periods are controlled by hormones in your body. Anything that could potentially throw your hormone levels into imbalance can trigger a change to your cycle: Causing either early or late periods.
Certain hormones respond to the amount of carbohydrates you consume - so someone that is dropping the pounds is likely cutting down on carbs, and this has a well established effect on periods.
Gaining weight can affect your period cycle too, as your body begins producing more hormones because of this change.
Even physical exercise like going to the gym can impact the timing of your period.
So if you've been losing weight and are worried about your period coming on earlier than expected - I can assure you it's normal!