FPGAs (Field Programmable Gate Arrays) are making their way into data centers (DCs) and are used to offload and accelerate specific services, but they are not yet available to cloud users. This puts the cloud deployment of compute-intensive workloads at a disadvantage compared with on-site infrastructure installations, where the performance and energy efficiency of FPGAs are increasingly being exploited for application-specific accelerators and heterogeneous computing. The cloud is housed in DCs, and DCs are based on ever shrinking servers. Today, we observe the emergence of hyper scale data centers, which are based on densely packaged servers. The shrinking form factor brings the potential to deploy FPGAs on a large scale in such DCs. These FPGAs must be deployed as independent DC resources, and they must be accessible to the cloud users. Therefore, we propose to change the traditional paradigm of the CPU-FPGA interface by decoupling the FPGA from the CPU and connecting the FPGA as a standalone resource to the DC network. This allows cloud vendors to offer an FPGA to users in a similar way as a standard server. As existing infrastructure-as-a-service (IaaS) mechanisms are not suitable, we propose a new Open Stack (open source cloud computing software) service to integrate FPGAs in the cloud. This proposal is complemented by a framework that enables cloud users to combine multiple FPGAs into a programmable fabric. The proposed architecture and framework address the scalability problem that makes it difficult to provision large numbers of FPGAs. Together, they offer a novel solution for processing large and heterogeneous data sets in the cloud.