Kentucky native, Schramm, attended Western Kentucky University in Bowling Green, Kentucky, where he majored in English and became intensely involved in theater.
His college acting teacher urged him to apply for a four-year graduate scholarship to Juilliard's newly formed drama school in New York, which he won.
In the summer of 1988, Schramm traveled to California to co-star with Rebecca De Mornay in "Born Yesterday" at the Pasadena Playhouse, a highly acclaimed and popular production that brought him to the attention of Hollywood.
Since then, Schramm has worked steadily in television and film, guest-starring on numerous television series, including Jake and the Fatman in 1987, Wiseguy in 1987, The Equalizer in 1985, Miami Vice in 1984, and Spenser: For Hire in 1985.
He also provided the voice for one of the characters in the Disney animated series Hercules in 1998 and had leading roles in The Time of Your Life in 1976 and the musical Cradle Will Rock in 1999, both for PBS.
