Short answer: No. Historical samurai did not have tattoos as a cultural practice.

Tattoos in Feudal Japan

In Edo-period Japan (1603-1868), tattoos (irezumi) had a specific and stigmatised social meaning: they were used to mark criminals. Courts sentenced convicted criminals to tattoos — typically on the face or forearm — as permanent visible punishment. The tattoo announced to anyone who saw it that the bearer had been convicted of a crime. [history]

For a samurai — a member of the warrior class whose identity, reputation, and social standing were everything — being tattooed would have been equivalent to being branded a criminal. The idea that samurai would voluntarily get tattoos as a form of warrior identity would have been deeply alien to their honour culture. [history]

Where Decorative Tattooing Did Develop

A separate tradition of decorative tattooing (horimono) did develop in Edo Japan, but among non-samurai populations: labourers, firefighters (tobi), and those living in the lower social margins. The elaborate full-body decorative tattoo tradition that later became internationally famous is associated with these groups and, increasingly, with the yakuza (organised crime) in the late Edo and Meiji periods. [history]

The yakuza tattoo tradition — elaborate, covering the torso and limbs — developed partly because covering the criminal punishment tattoo (by surrounding it with decorative work) was a practical concern, and partly as a cultural marker of belonging to a group that operated outside mainstream society. [history]

Why the Myth Exists

The idea of tattooed samurai is a collision of two aesthetically striking Japanese visual traditions: samurai imagery and Japanese tattoo art. Both have been enthusiastically received in Western popular culture, and they have been merged in ways that have no historical basis. [contested]

Manga, anime, films, and games featuring samurai characters with tattoos have spread this image widely. Western tattoo culture’s enthusiasm for Japanese imagery — both samurai motifs and irezumi-style designs — has reinforced it. [history]

The historical reality is straightforward: samurai and tattoos occupied opposite ends of the Edo-period social scale. Warriors were the honoured class; tattoos were the mark of the criminal class. Combining them would have made no sense to anyone living in the actual historical period.