The short answer is that a version of fortune telling was, and in some cases still is, a traditional occupation for Romani women. The type with crystal balls, "gypsy curses," and heavily relying on Tarot cards is a fictitious stereotype.
A little background on cultural history: many elements of Romani cultures seem to be inherited from early South Asian traditions and heavily influenced by the countries in which a group has migrated through/primarily settled. Traditional elements of Romani fortune telling are thus things like reading tea leaves/coffee grounds and palm reading. Most contemporary Roma I know have family traditions in tea and coffee readings.
As I've mentioned in previous comments on here, Romani people were itinerant or semi-itinerant for lots of reasons. One of those reasons was economics; for example, if your family are primarily copper smiths, it makes more sense to travel town-to-town to sell your wares or contract for work than to sit in one place and sell to the same people over and over. For women, fortune telling was a way to help earn money for her family on the move. This isn't to imply that these aspects of fortune telling lack intrinsic value (many are rooted in Romani spiritual traditions), it's only meant to say that fortune telling as a trade is the reason why it was exposed to non-Roma.
The trade served a couple other purposes too. Alexandra Oprea, a Romanian Roma law student and activist, compares the intimate interactions in Roma fortune telling as something comparable to therapy, where a client talks about their problems and the fortune teller offers validation.
Tarot isn't inherently Romani (there's variations that predate the Romani diaspora and iirc the most common forms used today originated in Italy in the 15th century), but it was adopted by a lot of Romani fortune tellers. Edit: I've recently seen from other Roma that their families do have spiritual traditions surrounding cartomancy and specifically Tarot. This is my error. Romani cultures are incredibly diverse, and when discussing traditions it's a walking a tightrope between inclusion and not overgeneralizing. Some subgroups and families do their best to distance themselves from Tarot and are adamant it's not Romani at all; others do insist it's a core part of Romani culture. I should qualify that I'm as good as gadje on this subject (my family had nothing to do with cards and fortune telling was shunned as soon as my Roma side immigrated to the U.S.) so I can only speak to what I've witnessed from others' traditions and what I know of the historic record.
Crystal balls have never been Romani specifically, and unfortunately I have no idea where that comes from. I assume it was a case of the crystal ball gaining popularity as a divination tool during the Spiritualism movement in the 19th-20th centuries, steadily evolved into a "fortune teller" stereotype, and the stereotype was then applied to Romani women. There are of course actual divination traditions that use crystals, I'm just not aware of any Roma whose families have used them.
Now there's all sorts of spiritual traditions that fall under the "fortune teller" umbrella, like the 19th century Spiritualism movement and certain Afro-Carribean traditions. So why is fortune telling so heavily associated with Romani people?
Roma were (and are) heavily discriminated against across Europe. Fortune telling became a convenient bridge to the "witch" archetype, a false stigma that carried over to the New World as Romani were imprisoned, expelled to European colonies, and at times enslaved. Despite the fact that Romani spirituality is compatible with and even incorporates elements of dominant religions (ex: Sara e Kali, the Patron Saint of Romani, is derived from the Hindu goddess Kali and Catholic saints), Roma people have been consistently seen as the Other.