Analysis of large-scale sequential data has been one of the most crucial tasks in areas such as bioinformatics, text, and audio mining. Existing string kernels, however, either (i) rely on local features of short substructures in the string, which hardly capture long discriminative patterns, (ii) sum over too many substructures, such as all possible subsequences, which leads to diagonal dominance of the kernel matrix, or (iii) rely on non-positive-definite similarity measures derived from the edit distance. Furthermore, while there have been works addressing the computational challenge with respect to the length of string, most of them still experience quadratic complexity in terms of the number of training samples when used in a kernel-based classifier. In this paper, we present a new class of global string kernels that aims to (i) discover global properties hidden in the strings through global alignments, (ii) maintain positive-definiteness of the kernel, without introducing a diagonal dominant kernel matrix, and (iii) have a training cost linear with respect to not only the length of the string but also the number of training string samples. To this end, the proposed kernels are explicitly defined through a series of different random feature maps, each corresponding to a distribution of random strings. We show that kernels defined this way are always positive-definite, and exhibit computational benefits as they always produce Random String Embeddings (RSE) that can be directly used in any linear classification models. Our extensive experiments on nine benchmark datasets corroborate that RSE achieves better or comparable accuracy in comparison to state-of-the-art baselines, especially with the strings of longer lengths. In addition, we empirically show that RSE scales linearly with the increase of the number and the length of string.