What are the rules on semi-colons?

Cruise ships can stay in one port for a short time only; which can be a problem if one wants to stay longer.

Can I use a semi-colon in this sentence of two halves?

You sure can, the relative clause introduced by which is supplementary and so allows a pause in prosody marked in writing by a comma or a semi-colon. However, it is more common to use a semi-colon when the parts of the sentence to the left and/or right of the semicolon have commas contained in them.

Some examples of this construction:

Snakes are cold-blooded animals; which means that their body temperature is about the same as the temperature of their surroundings.(Zoology; A.M. Winchester, Harvey B. Lovell; D. Van Nostrand Company, Inc. Princeton)

Not into young Pierre, did there then steal that thought of utmost sadness; pondering on the inevitable evanescence of all earthly loveliness; which makes the sweetest things of life only food for ever-devouring and omnivorous melancholy. (Pierre or, The Ambiguities; Herman Melville)

Were there no such replies as these to Mr. Froude's reasons, there would still be the reply furnished by his own interpretations of history ; which make it clear that his denial must be understood as but a qualified one. (On Social Evolution; Herbert Spencer; The University of Chicago Press, Chicago, 1972)

These little informal soviets elect a local soviet ; which elects delegates to the city or country (community) soviet ; which elects delegates to the government (State) soviet. ( The Nation: 10/4/1919, Vol. 109 Issue 2831, p479-482, 4p)

We have no idea what she looked like, for no portrait of her is known to exist and not a single one of her contemporaries ever described her physical appearance; which leads one to suspect that she was neither beautiful nor ugly, but rather plain. (ACAD: History Today; The Lady and the Earl; Greig, Martin; Sep2010, Vol. 60 Issue 9, p17-23, 7p, 9 Color Photographs)

People of quality do not work with their hands; which said, was enough to put artists in their place. (ACAD: Art Bulletin; Dec93, Vol. 75 Issue 4, p583, 16p, 3bw)