I'm not sure how strong the correlations are or if the relationship holds for some type of alcohol consumption or recreational drug use versus abstention from all of them, or if the correlation holds in varying degrees for alcohol and each drug considered separately (only the abstract is freely accessible). Based on GSS responses and a United Health Foundation report, alcohol consumption and IQ appear to be positively correlated.
Recreational drug usage is a topic for which the GSS contains a relevant question as well, so why not see if it supports what the journal article found? The percentage of respondents who have ever injected illicit drugs by intelligence grouping*. To allow ample time for experimentation to have occurred, only those aged 30 or older are included. For contemporary relevance, all responses are from 2002 or later (n = 9,892):
This doesn't include smoking weed, the most easily attainable and frequent form of recreational drug use in the US. That said, the modest relationship is, in contrast to the article's finding, inversely correlated with intelligence.
I wonder how important the specific drug in question is to detecting a relationship between usage and intelligence. Presumably crack cocaine users tend to be less intelligent than powdered users are (although as crack is a predominately black drug and powdered cocaine a predominately Hispanic one, neither may correlate positively with intelligence). I'd guess that meth use and intelligence, if anything, trend in opposite directions, as the stereotypical methhead is a rustic white prole of the lowest order. PCP, shrooms, LSD, and ecstasy, on the other hand, are fairly prevalent on college campuses. I know people who use or have used all of them, and they're mostly well-adjusted and intelligent folks. I don't have much of an impression one way or the other when it comes to heroin. The Chinese liked it and it seems pretty popular in Europe, but I'm aware of heroin users who are of cut from the same cloth as methheads, too.
Parenthetically, I've never had even the slightest desire to engage in illicit drug use of any kind. I've associated it with being sickly and desperate for as long as I can remember, and always avoided it without issue even during my formative years. On personality tests, I come up around the 40th percentile on openness, so that bit of built-in protection might help a little, too!
GSS variables used: EVIDU, WORDSUM, AGE(30-89)
* Respondents are broken up into five categories that come to roughly resemble a normal distribution; Really Smarts (wordsum score of 9-10, comprising 13% of the population), Pretty Smarts (7-8, 26%), Normals (6, 22%), Pretty Dumbs (4-5, 27%), and Real Dumbs (0-3, 12%)