Cinci has been a Teamster in Local 243 since 1969, originally employed by Montgomery Wards. While at Wards he served as a Steward for six years. In 1979 he accepted full time employment as a Business Agent with Local 243. As a Business Agent, Cinci has been involved in every contract that the Local administers.

Cinci has served as a member of the Montgomery Wards National Negotiating Committee since 1980 and later became Chairman of the National Negotiating Committee in 1994.

In 1997 he served on the Teamsters UPS National Negotiating Committee and the Central Region Negotiating Committee and on the Teamsters UPS National Negotiating Committee once again in 2002.

As Chairman of the Local's Organizing Committee he helped organize several hundred new members.