The answer to your question depends on the time. Anytime after 1860 the Republican Party existed.
Robert Taft
Grover Cleavland and Walter Mandale were not members of the Republican Party.
Scalawags
Bob Dole
republican
Thaddeus Stevens and Charles Sumner
The Democratic-Republican Party was better known as the Republican Party. The later Republican Party was named to pay homage to this party.
Woodrow Wilson
Martha McCollum is a Republican. She is known for her conservative viewpoints and has been involved in various Republican political activities and campaigns.
There are several well known Republican quotes. These quotes include "Latinos are Republic. They just don't know it yet," and "The father is always a Republican toward his son, and his mother's always a Democrat."
He's a republican.
The Republican Party is also known as the Grand Old Party (GOP).