Absent further clarification in the question, we might first have to differentiate between:
1. the first car with an electric lighter ("installed/wired in"?),
2. with such a lighter as standard equipment,
3. with a lighter executed as a "receptacle",
4. with a lighter receptacle standardised?
The cases 1 and 2 might result completely different results than 3 and 4. The earliest electric lighters were usually on a cord, bringing the heater element in direct contact with the to be lit material while still being connected to power. Cases 3 and 4 made power and heating element detachable so that the actual lighter was then realised as a plug that became standardised in the 50s and is now the "receptacle" that is said to be on the way of being phased out.
One stationary example with a non-detachable cord from the 20s:
According to the article Zigarettenanzünder: Geschichte und Funktionsweise,
Erst in den 1920er Jahren setzte sich die Bezeichnung
„Zigarettenanzünder“ durch – mit zunehmender Modernität der Zigarette.
Etwa zu dieser Zeit wurden auch die ersten Fahrzeuge mit dieser
Funktion ausgestattet – zunächst in den USA.
Translation: It was only in the 1920s that the term "cigarette lighter" prevailed - with the cigarette becoming more modern. Around this time, the first vehicles were equipped with this feature - initially in the US.
Given the above, it would seem very likely that the first car 'to come with a cigarette lighter' was the Lincoln L model in 1920 (as mentioned by called2voyage in the comment above):
The Lincoln L model was introduced in 1920 and was powered by a 357.8
cubic-inch V8 engine producing 90 horsepower, riding on a 130 inch
wheelbase and weighing in at 2490 pounds. It was priced at $4,300. The
large body built by Murray features unique features such as a 'fat
man' steering wheel that folds out of the way for ease of entry and a
cigar lighter that extends from a reel to reach throughout the
The phrase "extends from reel to reach throughout the interior" would make that car fall into the category of1 and 2, not of the recepetacle/plug type.
There is also a reference in Car: The Definitive Visual History of the Automobile to 'cigar lighter' in the 1922 Lincoln L sedan.
According to a link provided by LangLangC,
Zuvor waren laut der Zeitschrift „Oldtimer Markt“ aber bereits Nachrüstlösungen verfügbar. Bereits seit 1907 bot AEG etwa ein Gerät mit einem Platinglühdraht an, der sich auf Knopfdruck erhitzte.
Translation: …retrofit solutions were already available, according to the magazine "Oldtimer Markt". Already since 1907, AEG offered a device with a platinum glow wire, which heated itself at the push of a button.
This, though, was an 'optional extra' rather than a feature. This article also says a 1924 Cadillac had the first cigar lighter, but it seems the writer missed the Lincoln L (for which there are two sources).
So this leaves a bit room for confusion over terms. ––– According to Jason Torchinsky: "A Tribute To The Cigarette Lighter Plug, The Original Car Hack"
Early ones had a heating element connected by an extendible cord, but these were ungainly and awkward — getting the cord reeled back in couldn't have always been easy. Getting rid of that cord was key, and the earliest patent I found that seems to have achieved this design was filed on October 2, 1919 — the birthday of both my sister and Mahatma Ghandi.