There are 2 reasons.

The oxidants in each toxic puff of a cigarette not only wreck your lungs and age your skin, but also damage the internal ‘skin’ of the throat. This makes the throat lose its elasticity — giving you in effect an internal turkey neck which wobbles as you breathe, making the snoring sound [1].

The other reason for why smokers snore is the mucus that coats the throat and nose. Smokers are, in effect, allergic to cigarette smoke [2], so the body does its best to protect itself from the damage by producing a layer of mucus. This then vibrates as the smoker sleeps, causing more of the snoring sound.

Clearly, the answer for snorers who smoke is to give up smoking. In the meantime, take a strong anti-oxidant supplement containing vitamins A, C, E and beta-carotene, plus zinc, selenium, glutathione and cysteine.

You could also try the two anti-snore sprays Snor Away and Neversnore.

References:

[1] Virkkula P, Hytönen M, Bachour A, Malmberg H, Hurmerinta K, Salmi T, Maasilta P. Smoking and improvement after nasal surgery in snoring men.  PMID: 17424873.

[2] Walter S, Jeyaseelan L. Impact of cigarette smoking on pulmonary function in non-allergic subjects. PMID: 1302579.