Giuseppe "Peppe" Carta was born on December 3, 1912, in Bosa, on the island of Sardinia. His father, Attilio Carta, worked as a tax inspector and also played flute with the Cagliari Symphony Orchestra, and his older brother Mario Carta likewise became a working musician. The family moved to Rome in 1926. After hearing a jazz orchestra play in the city's Villa Borghese park in the summer of 1928, the teenage Carta asked his father for a double bass. He studied violin in Rome under the maestro Zuccarini at the Filarmonica school before turning fully to the bass, which he trained on formally at Rome's Santa Cecilia Conservatory after earlier study at the Cagliari Conservatory.

He moved quickly into Italy's dance-orchestra circuit: in 1932 he played in the Casanova club orchestra, directed by Bios Vercelloni, at the Venice International Film Festival. Later in the decade he worked in orchestras led by Gorni Kramer, Enzo Ceragioli and Piero Morgan, three of the bandleaders who shaped Italian swing in the years before the Second World War. Military service took him to Ethiopia between 1934 and 1937, including a posting at a telegraph office in Adua.

At the end of 1939 and into early 1940, Carta and his brother joined a symphonic ensemble, drawn partly from the orchestra of Milan's Teatro alla Scala, that performed at the New York World's Fair. Multiple Italian jazz-historical accounts describe the engagement putting him in direct contact with major American jazz figures of the period, among them Louis Armstrong, Benny Goodman, Billie Holiday and Frank Sinatra. Italy's declaration of war in June 1940 closed the Italian pavilion and complicated the ensemble's return home.

Carta was in Rome when Allied forces, including the U.S. Fifth Army, entered the city in June 1944; a surviving photograph places him on double bass at a jam session with Fifth Army musicians at the Galleria San Marco on Via del Babuino that year. In 1945 he worked in a trio with singer-pianist Bruno Martino and guitarist Libero Tosoni, and took part in a December 8 jazz concert at Rome's Teatro Quattro Fontane, one of the city's first organized postwar jazz events. In the early 1950s he relocated to Bogotà, Colombia, where he led his own ensemble, billed on later reissues as Orquesta Carta Musical, before returning to Italy.

Back in Rome, Carta resumed recording as a bassist from 1958, the year a Radiocorriere photograph placed him in singer-bandleader Lelio Luttazzi's sestet alongside vibraphonist Franco Chiari, guitarist Libero Tosoni, clarinetist Bill Smith and drummer Roberto Podio. In 1960 he played double bass on Piero Umiliani's big-band session issued as Tempo Jazz (RCA Custom), and in 1963 his double-bass work on Umiliani's "Sequenze Ritmiche" was selected for 40 Anni Di Jazz In Italia, the two-LP historical anthology of Italian jazz assembled by jazz historian Adriano Mazzoletti for the Ricordi label. He recorded through the 1960s in Franco Chiari's own jazz quartet, documented on two Radio Records releases (1966 and 1968), and in 1969 and 1970 played bass on two albums by the Trio Di Roberto Pregadio. Through this period he also worked in RAI's light-music orchestra and was active with Rome's musicians' union.

From around 1969 to 1972, Carta additionally worked as an orchestra conductor on a run of library-music albums for the Metropole Records and Lupus Records catalogues, several made with composer Stefano Torossi, including Musica Per Tutte Le Età, Ora Beat! and Fantasia Musicale, and one under his own sole billing, Ventaglio Musicale (1971). He kept contributing to Italian film scores into the 1960s and 1970s, including Piero Umiliani's A Cavallo Della Tigre (1967), and material from his sessions with Umiliani has continued to surface on archival soundtrack and library-music reissues into the 2020s. Carta remained active in Rome's music scene until his death there in July 1997, at age 84.

Carta's recorded credits sit squarely in Italian jazz's swing and big-band era: Discogs tags his sessions Big Band, Dixieland and Swing, and his working relationships ran through the bandleaders who defined that sound in Italy, from Gorni Kramer's prewar orchestra to Piero Umiliani's postwar big band. As a bassist for hire he moved between straight jazz dates, such as Umiliani's Tempo Jazz, Franco Chiari's quartet and the Trio Di Roberto Pregadio, and the broader dance-orchestra and radio-orchestra work that sustained most working Italian musicians of his generation. In the later part of his career he stepped from the bass stool to the conductor's podium for a run of library-music albums made mainly for Italian radio and television use, a common second career for jazz-trained musicians of his era; several of the LPs he directed still carry a Jazz tag on Discogs alongside easy-listening, funk and pop material.