Twitter has become an important platform for geo-spatial analyses, providing high-volume spatial data on a wide variety of social processes. Understanding the relationship between population density and Twitter activity is therefore of key importance. This study reports a systematic relationship between population density and Twitter use. Number of tweets, number of users and population per unit area are related by power law functions with exponents greater than one. These relations are consistent with each other and hold across a range of spatial scales. This implies that population density can accurately predict Twitter activity, but importantly, it also implies that correct predictions are not given by a naive linear scaling analysis. The observed super-linearity has implications for any spatial analyses performed with Twitter data and is important for understanding the relationship between Twitter use and demographics. For example, the robustness of this relationship means that we can identify 'anomalous' geographic areas that deviate from the observed trend, identifying several towns with high/low usage relative to expectation; using the scaling relationship we are able to show that these anomalies are not caused by age structure, as has been previously proposed. Proper consideration of this scaling relationship will improve robustness in future geo-spatial studies using Twitter.