For effectively searching the Web of data, ranking of results is a crucial. Top-k processing strategies have been proposed to allow an efficient processing of such ranked queries. Top-k strategies aim at computing k top-ranked results without complete result materialization. However, for many applications result computation time is much more important than result accuracy and completeness. Thus, there is a strong need for approximated ranked results. Unfortunately, previous work on approximate top-k processing is not well-suited for the Web of data. In this paper, we propose the first approximate top-k join framework for Web data and queries. Our approach is very lightweight necessary statistics are learned at runtime in a pay-as-you-go manner. We conducted extensive experiments on state-of-art SPARQL benchmarks. Our results are very promising: we could achieve up to 65% time savings, while maintaining a high precision/recall.