More commonly, a suspect would be read his rights at or shortly after the time of his arrest. However, this would only be an issue if he made some statement which tended to implicate or incriminate himself (e.g. a confession) prior to being told of his relevant rights (such as to remain silent, to an attorney, etc.). If he did not make any such statement before being told his rights, then the delay in reading his rights is most likely "harmless error" that will not affect his prosecution.