No. People with tattoo can donate blood. However, if you had your tattoo in a facility (shop) where they reuse ink for their clients or you had your tattoo in a facility operating without government license. Then you will have to wait for about a year before you can donate blood.
This is done in order to prevent transmitting infections such hepatitis, or infections with longer incubation period.
But if you had your tattoo in a licensed facility, you can donate blood anytime.