The user u/idjet provides a very thorough explanation of the major writer that puts forward this theory, Mary Kilbourne Matossian. Check that out for a thorough analysis of whether these claims hold up.

I think it's interesting to follow the history of this idea. As far as I have been able to find, the idea was first raised in 1976 in the journal Science by Linda R. Caporael in an article titled "Ergotism: The Satan Loosed in Salem?". Later that year, Jack Gottlieb and Nicholas Spanos published a refutation in that same journal, titled "Ergotism and the Salem Village Witch Trials." In their refutation, they point out that the distribution of affected people seems wrong for an ergot outbreak, as do the symptoms reported. To quote their conclusions: "The available evidence does not support the hypothesis that ergot poisoning played a role in the Salem crisis. The general features of the crisis did not resemble an ergotism epidemic. The symptoms of the afflicted girls and of the other witnesses were not those of convulsive ergotism. And the abrupt ending of the crisis, and the remorse and second thoughts of those who judged and testified against the accused, can be explained without recourse to the ergotism hypothesis" (1394).

Matossian published an article "Ergotism and the Salem Witchcraft Affair" in 1982, and then expounded her theories in the book described by u/idjet in 1989 to include other cases she ascribes to ergotism and other poisonings. In the article (I'll leave addressing the book to u/idjet) she specifically addresses the article by Spanos and Gottlieb, saying "this objection is not as valid as originally perceived" (355). Her article insists that contemporary accounts match ergot symptoms, but she does not provide a thorough, separate explanation for what are considered ergot poisoning symptoms. One can assume it does not usually include a vision of a "multitude in white glittering robes" (356). She acknowledges that the records do not mention many of the symptoms of ergot poisoning, but suggests the records may simply have left them out, and she also says that the records do not show whether victims had relapses (another symptom of ergot poisoning). She associates accusers clearly being stimulated by social cues in the courtroom (one girl's attack setting off the rest, girls reacting to accused witches, etc.) to the suggestibility of those affected by lycergic acid diethylamide (LSD), "which some mycologists believe can occur in a natural state" (356).

In 1983, Spanos (just Spanos this time) responded to Matossian in the article "Ergotism and the Salem Witch Panic". He is so dismissive it's worth quoting him directly: "I will show that she [Matossian] does not present a single pertinent new fact in support of this hypothesis. The new information in her article is either irrelevant to the ergot hypothesis, incorrect, or presented in a highly misleading manner. There is, in other words, not a shred of evidence in support of the ergot hypothesis" (358-359). Spanos takes exception to the lack of evidence cited by Matossian for her theories, which include that it was a cold winter in 1691, crops failed in 1692, and people turned to eating rye earlier than usual, which is why the witch panic "peaked in the summer of 1692" (359). He shoots down Matossian's claim about tree rings, showing that the ones she describes were not in the Salem area. He points out that Matossian citing an Ethiopian ergot outbreak as comparable misses that it was an outbreak of gangrenous ergotism, not convulsive ergotism, and also argues that her comparison of the rate of children affected from that incident is simply incorrect (360).

Spanos goes on to explain in detail symptoms ergot does not account for and also ergot symptoms not described in contemporary records. He shows that the descriptions of witchcraft are consistent with other contemporary accounts of witchcraft, including shapeshifting from human to animal, and that the children would convulse in the courtroom when an accused witch entered, one child's exclamation of something happening to her would trigger the rest, etc. He also cites accounts that accusers would appear completely healthy for long stretches between attacks, which is not consistent with ergot poisoning. He then goes into a long description of social factors affecting the accusations and describes contemporary accounts of demonic possession that show similar symptoms. He suggests mass hysteria as possibly related. He concludes with, "Understanding the demonic enactments, the pattern of accusations, and the legitimation of those accusations that occured in Salem requires that these events be viewed as part of a sociopolitical drama that was played out in terms of the implicit worldview and explicit religious assumptions that held sway among seventeenth-century Puritans" (367).

A 2000 study by Alan Woolf titled "Witchcraft of Mycotoxin? The Salem Witch Trials" in Clinical Toxicology agrees that ergot is unlikely to be the culprit, citing lack of data, symptom mismatch, and sociopolitical factors in Salem.

The theory pops up now and then as one of those "did you know?" trivia bits, but as far as I have read it is considered thoroughly disproven.

I realize this post is from two months ago, but thought you might find this interesting:

In April 1976, Science Magazine published an article by Linnda R. Caporael, the woman who came up with the ergot theory. (Though someone below credits Mary Kilbourne Matossian for the theory, I believe Caporael published her theory several years before Matossian began researching ergot.) A lady I know -- who was a member of the US Navy at the time -- read the article and immediately wrote Ms. Caporael, in care of the magazine, telling her the theory was erroneous. She (the friend) cited the fact ergot is an abortifacient and some of the accusing matrons at Salem, e.g., Mrs. Ann Putnam Sr. (a principal accuser) and Goodwife Bethshua Pope, were pregnant during the trials and both suffered from the characteristic "fits" exhibited by the "afflicted girls." On or about October 27, 1692, Mrs. Putnam gave birth to her seventh child, Abigail, and there is no indication the child was premature and she [the child] lived to age 51. Goody Pope gave birth to her seventh child, Ebenezer, December 4, 1692, and he, too, thrived. Ergot causes uterine contractions and had the Salem fits been the result of ergot poisoning, Mrs. Putnam and Goody Pope would have miscarried. Additionally, according to the records, the Salem Village birth rate did not decline in 1691/92.

Obviously, Ms. Caporael ingnored the letter and continued with her ergot poisoning theory. In 2001, she appeared on the PBS program Secrets of the Dead, still claiming ergot was the culprit in the Salem Witch Trials.