There is no commercial software that supports Thai handwriting. Thai handwritten character recognition is needed to convert handwritten text written on mobile and tablet devices into computer encoded text. We propose a novel method that joins three curve signatures. The first signature is the normalized tangent angle function (TAF), which provides rough classification. The other two novel curve signatures are the relative position matrix (RPM), used to compare global curve features, and the straightened tangent angle function (STAF), used to compare the tangent angle along the cumulative unsigned curvature domain. In the recognition process, an input curve is extracted for these three signatures and the similarity against each character in the handwriting templates is measured. Then, the similarity scores are weighted and summed for ranking. Our experiment is done on 48 handwriting samples (44 Thai consonants appear in each set, and there are 4 sets per handwriting). Our methods yield an accuracy of 93.89% for personal handwriting, and 91.33% for general handwriting.