No. The Amazon River basin is entirely in South America (Brazil, Peru, Colombia, Bolivia, Ecuador, Venezuela, Guyana, Suriname, French Guiana).
Costa Rica is in Central America, separated from South America by the Darién Gap (Panama-Colombia border). Its major rivers—San Juan (border with Nicaragua), Reventazón, Tempisque, Tárcoles—drain into the Caribbean Sea or Pacific Ocean, not the Amazon.