Dickenson was drafted in the 30th round of the 1968 Major League Baseball Draft by the San Francisco Giants out of Mesa Community College and the first round of the secondary phase of the 1969 draft by the Minnesota Twins out of Arizona State University. He was part of the 1969 College World Series championship Arizona State Sun Devils. He played minor league ball from 1969-1974 in the Twins chain, never advancing above Class A.
In 1969, Ralph hit .192/.256/.238 as an outfielder with the Red Springs Twins, producing just 16 runs in 50 games. He split 1970 between the St. Cloud Rox and Wisconsin Rapids Twins, improving to a composite .260 between the two stops. In '71, he batted .302 between the Orlando Twins and Auburn Twins, in limited action afield. He also pitched, going 7-5 with a 4.46 ERA for Auburn. He tied for 5th in the New York-Penn League in wins but also led in hits allowed (114), runs allowed (64) and tied for the most earned runs allowed (51).
Dickenson improved to 3-2 with a save and a 1.72 ERA in 16 games pitched for the 1972 Lynchburg Twins while hitting .280/.357/.360 in 200 at-bats. He fielded .970 in the outfield as a fine two-way player. With Lynchburg in '73, he was 8-8 with seven saves and a 3.10 ERA in 41 outings. Had he qualified, he would have been 8th in the Carolina League in ERA. He wrapped up his playing career still with Lynchburg in 1974, going 11-6 with four saves a 2.98 ERA in 56 games. He was 8th in the Carolina League in ERA, the only regularly-used reliever to make the top 10.
Dickenson was the head coach at Western Washington University in 1975-1978. He was the pitching coach for the Bellingham Dodgers in 1976 and managed the Grays Harbor Loggers in 1977. He also got into three games for the Loggers, getting a hit in his trip to the plate and losing his decision on the mound.
Dickenson was the Minor League Hitting Coordinator for the Seattle Mariners in 1990-1992 and Milwaukee Brewers in 1996-1997 in addition to managing assignments in 1988-1989 and 1993-1995. He was the Brewers' Minor League Field Coordinator in 1998-2000. He was Minor League Hitting Coordinator for the Los Angeles Dodgers in 2000-2001, Montreal Expos 2001-2002, and Texas Rangers 2002-2004. Dickenson was a minor league hitting coach for the New York Yankees in 2005-2006 and the Minor League Hitting Coordinator for the Washington Nationals 2007-2009. Dickenson was a coach for the New Hampshire Fisher Cats in 2010 and the Dunedin Blue Jays in 2011-2012.
- Trenton Thunder (January 26, 2006). "Article | MiLB.com News | The Official Site of Minor League Baseball". Milb.com. Retrieved October 26, 2013.
- "Rangers complete minor-league coaching staff | texasrangers.com: News". Texas.rangers.mlb.com. Retrieved October 26, 2013.
- "Archives | The Dallas Morning News, dallasnews.com". Nl.newsbank.com. April 24, 2004. Retrieved October 26, 2013.
- "Astros Announce 2014 Coaching Staff « CBS Houston". Houston.cbslocal.com. October 22, 2013. Retrieved October 26, 2013.
- Career statistics and player information from Baseball-Reference (Minors)