Born in Benidorm, Alicante, Valencian Community, Amor was a product of FC Barcelona's youth academy, and made his first-team debut in the 1988–89 season under Johan Cruyff, going on to become one of the Catalan team's most influential players as they achieved four consecutive La Liga titles and the 1991–92 European Cup (he did not play in the final against U.C. Sampdoria, however, after being booked in the last group stage match against S.L. Benfica). In 1993–94, as the club conquered the last of a successive four leagues, he appeared in all games except one, scoring a career-best eight goals. Additionally, on 5 April 1990, he opened the scoring in the Copa del Rey final against Real Madrid, helping to a 2–0 win at the Mestalla Stadium.