No, it is not accurate to say (based on that study) that 97% of experts agree that global warming is anthropogenic.
One problem is that there are two different definitions of "consensus" being used. The original consensus claim used by the IPCC was that it was very likely that most of the recent warming (>50%) was caused by humans. When we say that "global warming is anthropogenic" that is the common-sense definition people have in mind. Not simply that CO2 is a greenhouse gas that causes some unquantified amount of warming, but also that the amount of this warming is highly significant - that the biggest cause of warming is human activity in the form of releasing CO2.
The Cook study did not find 97% support for that proposition.
The study counted an article as "supporting the consensus" if it merely implicitly accepted that CO2 is a greenhouse gas. Since most skeptics accept that CO2 is a greenhouse gas, that doesn't tell us much we didn't already know - it uses too weak a definition of "consensus" to be useful.
Fortunately, the Cook et al database of rated abstracts is available to be searched on line. So we can check how many abstracts were in each sub-category, even though that info wasn't reported in the paper proper. (I've added links to queries that should return the actual abstract lists, so long as the database sticks around)
The Cook study gave papers a numeric rating. Rating #1 was "explicitly endorses and quantifies AGW as >50%". Out of 12,464 papers considered, only 65 papers were in this category (note: this was just based on study participants reading the abstracts, not the full paper).
Based on that statistic alone, one could defend the claim that one half of one percent of papers on AGW clearly claim humans are the chief cause of it. That headline finding would be "less than one percent of expert papers explicitly agree that global warming is anthropogenic."
But maybe it's not fair to include the "no position" papers. Let's exclude those. In that case, the headline finding is "1.5% (65/4215) of expert papers that took some position on global warming explicitly agree that global warming is anthropogenic."
The full list of endorsement categories were as follows:
- Explicitly endorses and quantifies AGW as >50% (65 articles)
- Explicitly endorses but does not quantify or minimize (934 articles)
- Implicitly endorses AGW without minimizing it (2934 articles)
- No position (8269 articles)
- Implicitly minimizes or rejects AGW (53 articles)
- Explicitly minimizes or rejects AGW but does not quantify (15 articles)
- Explicitly minimizes or rejects AGW as less than 50% (10 articles)
If we sum the rejection categories 5-7 together, there were 78 articles rejecting AGW, versus only 65 explicitly supporting the consensus. So another defensible headline finding is: "More articles implicitly or explicitly reject AGW than claim more than half of AGW is anthropogenic."
Or we could look at JUST the papers that give an explicit numeric percentage estimate. Comparing category 1 with category 7, we get this defensible headline: "87% of scientific articles that give a percentage estimate claim more than half of warming is anthropogenic". (though it would be important to note the actual number of articles in that case isn't much of a sample: 65 for versus 10 against).
Or if we want to rescue the original Cook number, that can be accomplished by adding a few caveats. Like so: "97% of articles on global warming that take a position on the matter either implicitly or explicitly endorse that human activity is causing some global warming"
Since the vast majority (98.5%) of these papers don't quantify how much warming, that's about as far as we can go.